compact abelian groups: Topics by Science.gov

Sample records for compact abelian groups

On spectral synthesis on element-wise compact Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2015-08-01

Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ_y\\colon f(x)\\mapsto f(xy), y\\in G. By definition, an invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis if \\mathscr H coincides with the closure in C(G) of the linear span of all characters of G belonging to \\mathscr H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace \\mathscr H\\subseteq C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
Localization in abelian Chern-Simons theory

NASA Astrophysics Data System (ADS)

McLellan, B. D. K.

2013-02-01

Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed using the technique of non-abelian localization. This study leads to a natural identification of the abelian Reidemeister-Ray-Singer torsion as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections for the class of Sasakian three-manifolds. The torsion part of the abelian Chern-Simons partition function is computed explicitly in terms of Seifert data for a given Sasakian three-manifold.
On spectral synthesis on zero-dimensional Abelian groups

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2013-09-01

Let G be a zero-dimensional locally compact Abelian group all of whose elements are compact, and let C(G) be the space of all complex-valued continuous functions on G. A closed linear subspace \\mathscr H\\subseteq C(G) is said to be an invariant subspace if it is invariant with respect to the translations \\tau_y\\colon f(x)\\mapsto f(x+y), y\\in G. In the paper, it is proved that any invariant subspace \\mathscr H admits spectral synthesis, that is, \\mathscr H coincides with the closed linear span of the characters of G belonging to \\mathscr H. Bibliography: 25 titles.
Topology-preserving quantum deformation with non-numerical parameter

NASA Astrophysics Data System (ADS)

Aukhadiev, Marat; Grigoryan, Suren; Lipacheva, Ekaterina

2013-11-01

We introduce a class of compact quantum semigroups, that we call semigroup deformations of compact Abelian qroups. These objects arise from reduced semigroup -algebras, the generalization of the Toeplitz algebra. We study quantum subgroups, quantum projective spaces and quantum quotient groups for such objects, and show that the group is contained as a compact quantum subgroup in the deformation of itself. The connection with the weak Hopf algebra notion is described. We give a grading on the -algebra of the compact quantum semigroups constructed.
An uncertainty principle for unimodular quantum groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crann, Jason; Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d'Ascq Cédex; Kalantar, Mehrdad, E-mail: jason-crann@carleton.ca, E-mail: mkalanta@math.carleton.ca

2014-08-15

We present a generalization of Hirschman's entropic uncertainty principle for locally compact Abelian groups to unimodular locally compact quantum groups. As a corollary, we strengthen a well-known uncertainty principle for compact groups, and generalize the relation to compact quantum groups of Kac type. We also establish the complementarity of finite-dimensional quantum group algebras. In the non-unimodular setting, we obtain an uncertainty relation for arbitrary locally compact groups using the relative entropy with respect to the Haar weight as the measure of uncertainty. We also show that when restricted to q-traces of discrete quantum groups, the relative entropy with respect tomore » the Haar weight reduces to the canonical entropy of the random walk generated by the state.« less
Consistent Orientation of Moduli Spaces

NASA Astrophysics Data System (ADS)

Freed, Daniel S.; Hopkins, Michael J.; Teleman, Constantin

In a series of papers by Freed, Hopkins, and Teleman (2003, 2005, 2007a) the relationship between positive energy representations of the loop group of a compact Lie group G and the twisted equivariant K-theory Kτ+dimGG (G) was developed. Here G acts on itself by conjugation. The loop group representations depend on a choice of ‘level’, and the twisting τ is derived from the level. For all levels the main theorem is an isomorphism of abelian groups, and for special transgressed levels it is an isomorphism of rings: the fusion ring of the loop group andKτ+dimGG (G) as a ring. For G connected with π1G torsionfree, it has been proven that the ring Kτ+dimGG (G) is a quotient of the representation ring of G and can be calculated explicitly. In these cases it agrees with the fusion ring of the corresponding centrally extended loop group. This chapter explicates the multiplication on the twisted equivariant K-theory for an arbitrary compact Lie group G. It constructs a Frobenius ring structure on Kτ+dimGG (G). This is best expressed in the language of topological quantum field theory: a two-dimensional topological quantum field theory (TQFT) is constructed over the integers in which the abelian group attached to the circle is Kτ+dimGG (G).
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

DOE PAGES

Braun, Volker; Cvetič, Mirjam; Donagi, Ron; ...

2017-07-26

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less
Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braun, Volker; Cvetič, Mirjam; Donagi, Ron

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 X Z 2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of secondmore » cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.« less
Studying critical string emerging from non-Abelian vortex in four dimensions

DOE PAGES

Koroteev, P.; Shifman, M.; Yung, A.

2016-05-26

Recently a special vortex string was found in a class of soliton vortices supported in four-dimensional Yang–Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang–Mills theory has the U(2) gauge group and the Fayet–Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. Here, the full target space ismore » $$\\mathbb R$$ 4 x Y 6 where is a non-compact Calabi–Yau space.« less
FAST TRACK COMMUNICATION: \\ {P}\\ {T}-symmetry, Cartan decompositions, Lie triple systems and Krein space-related Clifford algebras

NASA Astrophysics Data System (ADS)

Günther, Uwe; Kuzhel, Sergii

2010-10-01

Gauged \\ {P}\\ {T} quantum mechanics (PTQM) and corresponding Krein space setups are studied. For models with constant non-Abelian gauge potentials and extended parity inversions compact and noncompact Lie group components are analyzed via Cartan decompositions. A Lie-triple structure is found and an interpretation as \\ {P}\\ {T}-symmetrically generalized Jaynes-Cummings model is possible with close relation to recently studied cavity QED setups with transmon states in multilevel artificial atoms. For models with Abelian gauge potentials a hidden Clifford algebra structure is found and used to obtain the fundamental symmetry of Krein space-related J-self-adjoint extensions for PTQM setups with ultra-localized potentials.
Introducing Abelian Groups Using Bullseyes and Jenga

ERIC Educational Resources Information Center

Smith, Michael D.

2016-01-01

The purpose of this article is to share a new approach for introducing students to the definition and standard examples of Abelian groups. The definition of an Abelian group is revised to include six axioms. A bullseye provides a way to visualize elementary examples and non-examples of Abelian groups. An activity based on the game of Jenga is used…
Projective loop quantum gravity. I. State space

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2016-12-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. Beside the physical motivations for this approach, it could help designing a quantum state space holding the states we need. In a latter work by Okolów, the description of a theory of Abelian connections within this framework was developed, an important insight being to use building blocks labeled by combinations of edges and surfaces. The present work generalizes this construction to an arbitrary gauge group G (in particular, G is neither assumed to be Abelian nor compact). This involves refining the definition of the label set, as well as deriving explicit formulas to relate the Hilbert spaces attached to different labels. If the gauge group happens to be compact, we also have at our disposal the well-established Ashtekar-Lewandowski Hilbert space, which is defined as an inductive limit using building blocks labeled by edges only. We then show that the quantum state space presented here can be thought as a natural extension of the space of density matrices over this Hilbert space. In addition, it is manifest from the classical counterparts of both formalisms that the projective approach allows for a more balanced treatment of the holonomy and flux variables, so it might pave the way for the development of more satisfactory coherent states.
Compact, singular G 2-holonomy manifolds and M/heterotic/F-theory duality

NASA Astrophysics Data System (ADS)

Braun, Andreas P.; Schäfer-Nameki, Sakura

2018-04-01

We study the duality between M-theory on compact holonomy G 2-manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G 2-manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G 2-manifolds we are able to identify the dual heterotic as well as F-theory realizations. First we establish this chain of dualities for smooth G 2-manifolds. This has a natural generalization to situations with non-abelian gauge groups, which correspond to singular G 2-manifolds, where each of the K3-fibers degenerates. We argue for their existence through the chain of dualities, supported by non-trivial checks of the spectra. The corresponding 4d gauge groups can be both Higgsable and non-Higgsable, and we provide several explicit examples of the general construction.
Critical non-Abelian vortex in four dimensions and little string theory

NASA Astrophysics Data System (ADS)

Shifman, M.; Yung, A.

2017-08-01

As was shown recently, non-Abelian vortex strings supported in four-dimensional N =2 supersymmetric QCD with the U(2) gauge group and Nf=4 quark multiplets (flavors) become critical superstrings. In addition to the translational moduli, non-Abelian strings under consideration carry six orientational and size moduli. Together, they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau noncompact threefold, namely, the conifold. We study closed string states which emerge in four dimensions and identify them with hadrons of four-dimensional N =2 QCD. One massless state was found previously; it emerges as a massless hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper, we find a number of massive states. To this end, we exploit the approach used in LST little string theory, namely, the equivalence between the critical string on the conifold and noncritical c =1 string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry "baryonic" charge (its definition differs from standard). We interpret them as "monopole necklaces" formed (at strong coupling) by the closed string with confined monopoles attached.
A very strong difference property for semisimple compact connected lie groups

NASA Astrophysics Data System (ADS)

Shtern, A. I.

2011-06-01

Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δ h f is defined by the rule Δ h f( x) = f( xh) - f( x) ( x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H( x + y) = H( x) + H( y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δ h f ∈ F for each h ∈ G, there is an additive function H such that f - H ∈ F. Erdős' conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional assumption that the other one-sided difference function ∇ h f defined by ∇ h f( x) = f( xh) - f( x) ( x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δ h f for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇ h f), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie groups.
Non-Abelian string and particle braiding in topological order: Modular SL (3 ,Z ) representation and (3 +1 ) -dimensional twisted gauge theory

NASA Astrophysics Data System (ADS)

Wang, Juven C.; Wen, Xiao-Gang

2015-01-01

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω4 of G 's cohomology group H4(G ,R /Z ) in three-dimensional space and one-dimensional time (3 +1 D ) . We establish the topological spin and the spin-statistics relation for the closed strings and their multistring braiding statistics. The 3 +1 D twisted gauge theory can be characterized by a representation of a modular transformation group, SL (3 ,Z ) . We express the SL (3 ,Z ) generators Sx y z and Tx y in terms of the gauge group G and the 4-cocycle ω4. As we compactify one of the spatial directions z into a compact circle with a gauge flux b inserted, we can use the generators Sx y and Tx y of an SL (2 ,Z ) subgroup to study the dimensional reduction of the 3D topological order C3 D to a direct sum of degenerate states of 2D topological orders Cb2 D in different flux b sectors: C3 D=⊕bCb2 D . The 2D topological orders Cb2 D are described by 2D gauge theories of the group G twisted by the 3-cocycle ω3 (b ), dimensionally reduced from the 4-cocycle ω4. We show that the SL (2 ,Z ) generators, Sx y and Tx y, fully encode a particular type of three-string braiding statistics with a pattern that is the connected sum of two Hopf links. With certain 4-cocycle twists, we discover that, by threading a third string through two-string unlink into a three-string Hopf-link configuration, Abelian two-string braiding statistics is promoted to non-Abelian three-string braiding statistics.
Non Abelian T-duality in Gauged Linear Sigma Models

NASA Astrophysics Data System (ADS)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; Santos-Silva, Roberto

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.
Non Abelian T-duality in Gauged Linear Sigma Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less
Non Abelian T-duality in Gauged Linear Sigma Models

DOE PAGES

Bizet, Nana Cabo; Martínez-Merino, Aldo; Zayas, Leopoldo A. Pando; ...

2018-04-01

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they dependmore » in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.« less
Radially separated classical lumps in non-Abelian gauge models

NASA Astrophysics Data System (ADS)

Burzlaff, Jürgen

1985-04-01

We search for smooth and time-independent finite-energy solutions to Yang-Mills-Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.

A Finite Abelian Group of Two-Letter Inversions

ERIC Educational Resources Information Center

Balbuena, Sherwin E.

2015-01-01

In abstract algebra, the study of concrete groups is fundamentally important to beginners. Most commonly used groups as examples are integer addition modulo n, real number addition and multiplication, permutation groups, and groups of symmetry. The last two examples are finite non-abelian groups and can be investigated with the aid of concrete…
Non-Abelian Gauge Theory in the Lorentz Violating Background

NASA Astrophysics Data System (ADS)

Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais

2018-03-01

In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.
General U(1)×U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structure

DOE PAGES

Cvetic, Mirjam; Klevers, Denis; Piragua, Hernan; ...

2015-11-30

We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1)×U(1) gauge symmetry. Generic U(1)×U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2)×SU(2)×SU(3), SU(2) 3×SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. Wemore » give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. In conclusion, the construction suggests a generalization to U(1) k factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups.« less
Direct Sum Decomposition of Groups

ERIC Educational Resources Information Center

Thaheem, A. B.

2005-01-01

Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
Lie-algebraic classification of effective theories with enhanced soft limits

NASA Astrophysics Data System (ADS)

Bogers, Mark P.; Brauner, Tomáš

2018-05-01

A great deal of effort has recently been invested in developing methods of calculating scattering amplitudes that bypass the traditional construction based on Lagrangians and Feynman rules. Motivated by this progress, we investigate the long-wavelength behavior of scattering amplitudes of massless scalar particles: Nambu-Goldstone (NG) bosons. The low-energy dynamics of NG bosons is governed by the underlying spontaneously broken symmetry, which likewise allows one to bypass the Lagrangian and connect the scaling of the scattering amplitudes directly to the Lie algebra of the symmetry generators. We focus on theories with enhanced soft limits, where the scattering amplitudes scale with a higher power of momentum than expected based on the mere existence of Adler's zero. Our approach is complementary to that developed recently in ref. [1], and in the first step we reproduce their result. That is, as far as Lorentz-invariant theories with a single physical NG boson are concerned, we find no other nontrivial theories featuring enhanced soft limits beyond the already well-known ones: the Galileon and the Dirac-Born-Infeld (DBI) scalar. Next, we show that in a certain sense, these theories do not admit a nontrivial generalization to non-Abelian internal symmetries. Namely, for compact internal symmetry groups, all NG bosons featuring enhanced soft limits necessarily belong to the center of the group. For noncompact symmetry groups such as the ISO( n) group featured by some multi-Galileon theories, these NG bosons then necessarily belong to an Abelian normal subgroup. The Lie-algebraic consistency constraints admit two infinite classes of solutions, generalizing the known multi-Galileon and multi-flavor DBI theories.
Scalability, Complexity and Reliability in Quantum Information Processing

DTIC Science & Technology

2007-03-01

hidden subgroup framework to abelian groups which are not finitely generated. An extension of the basic algorithm breaks the Buchmann-Williams...finding short lattice vectors . In [2], we showed that the generalization of the standard method --- random coset state preparation followed by fourier...sampling --- required exponential time for sufficiently non-abelian groups including the symmetric group , at least when the fourier transforms are
Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

2015-05-01

The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the Yang-Mills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator. Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole. We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gauge-invariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations. However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability group H ˜ of G, while there is a unique option of H ˜ = U(1) for G = SU(2) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for SU(3) , the maximal stability group is U(2) , which is different from the maximal torus group U(1) × U(1) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for SU(3) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the SU(2) case. Therefore, we claim that the mechanism for quark confinement for SU(N) (N ≥ 3) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.
Algebraic integrability: a survey.

PubMed

Vanhaecke, Pol

2008-03-28

We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kondo, Kei-Ichi; Shinohara, Toru; Kato, Seikou

2016-01-22

We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulationsmore » can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.« less
Reformulations of the Yang-Mills theory toward quark confinement and mass gap

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru

2016-01-01

We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N- 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1)N-1, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
S-duality in SU(3) Yang-Mills theory with non-abelian unbroken gauge group

NASA Astrophysics Data System (ADS)

Schroers, B. J.; Bais, F. A.

1998-12-01

It is observed that the magnetic charges of classical monopole solutions in Yang-Mills-Higgs theory with non-abelian unbroken gauge group H are in one-to-one correspondence with coherent states of a dual or magnetic group H˜. In the spirit of the Goddard-Nuyts-Olive conjecture this observation is interpreted as evidence for a hidden magnetic symmetry of Yang-Mills theory. SU(3) Yang-Mills-Higgs theory with unbroken gauge group U(2) is studied in detail. The action of the magnetic group on semi-classical states is given explicitly. Investigations of dyonic excitations show that electric and magnetic symmetry are never manifest at the same time: Non-abelian magnetic charge obstructs the realisation of electric symmetry and vice-versa. On the basis of this fact the charge sectors in the theory are classified and their fusion rules are discussed. Non-abelian electric-magnetic duality is formulated as a map between charge sectors. Coherent states obey particularly simple fusion rules, and in the set of coherent states S-duality can be formulated as an SL(2, Z) mapping between sectors which leaves the fusion rules invariant.
A reconstruction theorem for Connes-Landi deformations of commutative spectral triples

NASA Astrophysics Data System (ADS)

Ćaćić, Branimir

2015-12-01

We formulate and prove an extension of Connes's reconstruction theorem for commutative spectral triples to so-called Connes-Landi or isospectral deformations of commutative spectral triples along the action of a compact Abelian Lie group G, also known as toric noncommutative manifolds. In particular, we propose an abstract definition for such spectral triples, where noncommutativity is entirely governed by a deformation parameter sitting in the second group cohomology of the Pontryagin dual of G, and then show that such spectral triples are well-behaved under further Connes-Landi deformation, thereby allowing for both quantisation from and dequantisation to G-equivariant abstract commutative spectral triples. We then use a refinement of the Connes-Dubois-Violette splitting homomorphism to conclude that suitable Connes-Landi deformations of commutative spectral triples by a rational deformation parameter are almost-commutative in the general, topologically non-trivial sense.
Non-Abelian statistics of vortices with non-Abelian Dirac fermions.

PubMed

Yasui, Shigehiro; Hirono, Yuji; Itakura, Kazunori; Nitta, Muneto

2013-05-01

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined nonlocally by Majorana fermions located at two spatially separated vortices.
Master 3d bosonization duality with boundaries

NASA Astrophysics Data System (ADS)

Aitken, Kyle; Karch, Andreas; Robinson, Brandon

2018-05-01

We establish the action of the three-dimensional non-Abelian bosonization dualities in the presence of a boundary, which supports a non-anomalous two-dimensional theory. In particular, we generalize a prescriptive method for assigning duality consistent boundary conditions used originally for Abelian dualities to dual non-Abelian Chern-Simons-matter theories with SU and U gauge groups and fundamental matter sectors. The cases of single species matter sectors and those with both scalars and fermions in the dual theories are considered. Generalization of our methods to SO and USp Chern-Simons theories is also discussed.
Automorphisms of Order Structures of Abelian Parts of Operator Algebras and Their Role in Quantum Theory

NASA Astrophysics Data System (ADS)

Hamhalter, Jan; Turilova, Ekaterina

2014-10-01

It is shown that any order isomorphism between the structures of unital associative JB subalgebras of JB algebras is given naturally by a partially linear Jordan isomorphism. The same holds for nonunital subalgebras and order isomorphisms preserving the unital subalgebra. Finally, we recover usual action of time evolution group on a von Neumann factor from group of automorphisms of the structure of Abelian subalgebras.
Haag duality for Kitaev’s quantum double model for abelian groups

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter

2015-11-01

We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.
Composite particle theory of three-dimensional gapped fermionic phases: Fractional topological insulators and charge-loop excitation symmetry

NASA Astrophysics Data System (ADS)

Ye, Peng; Hughes, Taylor L.; Maciejko, Joseph; Fradkin, Eduardo

2016-09-01

Topological phases of matter are usually realized in deconfined phases of gauge theories. In this context, confined phases with strongly fluctuating gauge fields seem to be irrelevant to the physics of topological phases. For example, the low-energy theory of the two-dimensional (2D) toric code model (i.e., the deconfined phase of Z2 gauge theory) is a U(1 )×U(1 ) Chern-Simons theory in which gauge charges (i.e., e and m particles) are deconfined and the gauge fields are gapped, while the confined phase is topologically trivial. In this paper, we point out a route to constructing exotic three-dimensional (3D) gapped fermionic phases in a confining phase of a gauge theory. Starting from a parton construction with strongly fluctuating compact U(1 )×U(1 ) gauge fields, we construct gapped phases of interacting fermions by condensing two linearly independent bosonic composite particles consisting of partons and U(1 )×U(1 ) magnetic monopoles. This can be regarded as a 3D generalization of the 2D Bais-Slingerland condensation mechanism. Charge fractionalization results from a Debye-Hückel-type screening cloud formed by the condensed composite particles. Within our general framework, we explore two aspects of symmetry-enriched 3D Abelian topological phases. First, we construct a new fermionic state of matter with time-reversal symmetry and Θ ≠π , the fractional topological insulator. Second, we generalize the notion of anyonic symmetry of 2D Abelian topological phases to the charge-loop excitation symmetry (Charles ) of 3D Abelian topological phases. We show that line twist defects, which realize Charles transformations, exhibit non-Abelian fusion properties.
Approche Kaluza-Klein et Supersymetrie de Jauge

NASA Astrophysics Data System (ADS)

Pare, Jean-Pierre

This thesis presents a non-Abelian gauge-supersymmetric Kaluza-Klein approach for charged spinning particles and strings in a background of gravitational and Yang-Mills fields. In the classical Kaluza-Klein approach, the basic mathematical structure is a principal bundle of which the base manifold is space-time. This principal bundle is endowed with a pseudo-Riemannian metric, invariant under the action of the structural group of the bundle, and a connection. Geodesic equations on the bundle lead to the Maxwell-Lorentz equation for curved space-time and Yang -Mills fields, and to a conservation law of a non-Abelian (bosonic) charge. This conservation law originates from the invariance of the free-particle action on the bundle under the action of the structural group of the bundle (gauge group). Firstly, we generalize this approach for a spinning particle. The spin of the particle is described by Grassmannian variables added to the principal bundle. This supersymmetrization gives rise, in addition to the bosonic non-Abelian charge, a fermionic one. This leads to a search for a supergroup action on the superprincipal bundle which leaves invariant the action of the spinning particle. The invariance of this action would lead to the conservation of a non-Abelian super-charge, generalizing the conservation law obtained for particles without spin. We present Lagrangian and Hamiltonian formulations, both invariant under a super -group action. The equations of motion are derived and discussed. Different terms in these equations are well known in the literature. The invariance of these formulations under a supergroup action leads to a conservation law of a non-Abelian supercharge. The bosonic part of this supercharge corresponds to the non-Abelian (bosonic) charge obtained for a particle without spin. The fermionic part is a non -physical charge. It turns out in the supersymmetric case that this decouples from all other dynamical variables, and hence it does not influence trajectories of spinning particles. It is interesting to mention how this gauge -supersymmetry is introduced in the dynamics. It arises by choosing the unique metric connection on the principal bundle with torsion given by the Chern-Simons 3-form. We then proceed to extend these formulations for spinning strings. We present Lagrangian and Hamiltonian gauge-supersymmetric formulations in a superloop space setting. The same connection corresponding to the Chern -Simons 3-form is used here. Equations of motion are derived and discussed. In the appendix, we discuss the effect of using this connection in a non-Abelian Kaluza-Klein field theory. Using the same connection, we present a non-Abelian Kaluza-Klein approach leading to a zero cosmological constant.
Abelian gauge symmetries in F-theory and dual theories

NASA Astrophysics Data System (ADS)

Song, Peng

In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by constructing general F-theory compactifications with U(1) x U(1) x U(1) abelian gauge symmetry. In chapter 1 of this dissertation, I proved finiteness of a region of the string landscape in Type IIB compactifications. String compactifications give rise to a collection of effective low energy theories, known as the string landscape. In chapter 3 of this dissertation, I study abelian gauge symmetries in the duality between F-theory and E8 x E8 heterotic string theory. However, how abelian gauge symmetries can arise in the dual heterotic string theory has never been studied. The main goal of this chapter is to study exactly this. We start with F-theory compactifications with abelian gauge symmetry. With the help of a mathematical lemma as well as a computer code that I came up with, I was able to construct a rich list of specialized examples with specific abelian and nonabelian gauge groups on the F-theory side. (Abstract shortened by ProQuest.).
Non-Abelian sigma models from Yang-Mills theory compactified on a circle

NASA Astrophysics Data System (ADS)

Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.

2018-06-01

We consider SU(N) Yang-Mills theory on R 2 , 1 ×S1, where S1 is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on R 2 , 1 whose target space is a 2 (N - 1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU (N) ×SU (N) /ZN. The latter is the direct product of SU(N) and its Langlands dual SU (N) /ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.

Improved HDRG decoders for qudit and non-Abelian quantum error correction

NASA Astrophysics Data System (ADS)

Hutter, Adrian; Loss, Daniel; Wootton, James R.

2015-03-01

Hard-decision renormalization group (HDRG) decoders are an important class of decoding algorithms for topological quantum error correction. Due to their versatility, they have been used to decode systems with fractal logical operators, color codes, qudit topological codes, and non-Abelian systems. In this work, we develop a method of performing HDRG decoding which combines strengths of existing decoders and further improves upon them. In particular, we increase the minimal number of errors necessary for a logical error in a system of linear size L from \\Theta ({{L}2/3}) to Ω ({{L}1-ε }) for any ε \\gt 0. We apply our algorithm to decoding D({{{Z}}d}) quantum double models and a non-Abelian anyon model with Fibonacci-like fusion rules, and show that it indeed significantly outperforms previous HDRG decoders. Furthermore, we provide the first study of continuous error correction with imperfect syndrome measurements for the D({{{Z}}d}) quantum double models. The parallelized runtime of our algorithm is poly(log L) for the perfect measurement case. In the continuous case with imperfect syndrome measurements, the averaged runtime is O(1) for Abelian systems, while continuous error correction for non-Abelian anyons stays an open problem.
Index theorem for non-supersymmetric fermions coupled to a non-Abelian string and electric charge quantization

NASA Astrophysics Data System (ADS)

Shifman, M.; Yung, A.

2018-03-01

Non-Abelian strings are considered in non-supersymmetric theories with fermions in various appropriate representations of the gauge group U(N). We derive the electric charge quantization conditions and the index theorems counting fermion zero modes in the string background both for the left-handed and right-handed fermions. In both cases we observe a non-trivial N dependence.
Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

NASA Astrophysics Data System (ADS)

Matsudo, Ryutaro; Kondo, Kei-Ichi

2015-12-01

We give a gauge-independent definition of magnetic monopoles in the S U (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the S U (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.
Time evolution of complexity in Abelian gauge theories

NASA Astrophysics Data System (ADS)

Hashimoto, Koji; Iizuka, Norihiro; Sugishita, Sotaro

2017-12-01

Quantum complexity is conjectured to probe inside of black hole horizons (or wormholes) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for Abelian pure gauge theories. For this purpose, we discretize the U (1 ) gauge group as ZN and also the continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories and to evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ˜exp (entropy), which is one of the conjectured criteria necessary to have a dual black hole, the Abelian gauge theory needs to be maximally nonlocal.
Lattice implementation of Abelian gauge theories with Chern-Simons number and an axion field

NASA Astrophysics Data System (ADS)

Figueroa, Daniel G.; Shaposhnikov, Mikhail

2018-01-01

Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present an explicit non-compact lattice formulation of the interaction between a shift-symmetric field and some U (1) gauge sector, a (x)FμνF˜μν, reproducing the continuum limit to order O (dxμ2) and obeying the following properties: (i) the system is gauge invariant and (ii) shift symmetry is exact on the lattice. For this end we construct a definition of the topological number density K =FμνF˜μν that admits a lattice total derivative representation K = Δμ+ Kμ, reproducing to order O (dxμ2) the continuum expression K =∂μKμ ∝ E → ṡ B → . If we consider a homogeneous field a (x) = a (t), the system can be mapped into an Abelian gauge theory with Hamiltonian containing a Chern-Simons term for the gauge fields. This allow us to study in an accompanying paper the real time dynamics of fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. When a (x) = a (x → , t) is inhomogeneous, the set of lattice equations of motion do not admit however a simple explicit local solution (while preserving an O (dxμ2) accuracy). We discuss an iterative scheme allowing to overcome this difficulty.
Gauge-independent Abelian mechanism of color confinement in gluodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, Tsuneo; Ishiguro, Katsuya; Sekido, Toru

Abelian mechanism of non-Abelian color confinement is observed in a gauge-independent way by high precision lattice Monte Carlo simulations in gluodynamics. An Abelian gauge field is extracted with no gauge fixing. Then we decompose the Abelian field into regular photon and singular monopole parts using the Hodge decomposition. We find that only the monopole part is responsible for the string tension. The investigation of the flux-tube profile then shows that an Abelian electric field defined in an arbitrary color direction is squeezed by the monopole supercurrent with the same color direction, and the quantitative features of flux squeezing are consistentmore » with those observed previously after Abelian projections with gauge fixing. Non-Abelian color confinement is explained in the framework of the gauge-independent Abelian dual Meissner effect.« less
Universal moduli spaces of Riemann surfaces

NASA Astrophysics Data System (ADS)

Ji, Lizhen; Jost, Jürgen

2017-04-01

We construct a moduli space for Riemann surfaces that is universal in the sense that it represents compact Riemann surfaces of any finite genus. This moduli space is a connected complex subspace of an infinite dimensional complex space, and is stratified according to genus such that each stratum has a compact closure, and it carries a metric and a measure that induce a Riemannian metric and a finite volume measure on each stratum. Applications to the Plateau-Douglas problem for minimal surfaces of varying genus and to the partition function of Bosonic string theory are outlined. The construction starts with a universal moduli space of Abelian varieties. This space carries a structure of an infinite dimensional locally symmetric space which is of interest in its own right. The key to our construction of the universal moduli space then is the Torelli map that assigns to every Riemann surface its Jacobian and its extension to the Satake-Baily-Borel compactifications.
Competing ν = 5/2 fractional quantum Hall states in confined geometry.

PubMed

Fu, Hailong; Wang, Pengjie; Shan, Pujia; Xiong, Lin; Pfeiffer, Loren N; West, Ken; Kastner, Marc A; Lin, Xi

2016-11-01

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.
Relativized problems with abelian phase group in topological dynamics.

PubMed

McMahon, D

1976-04-01

Let (X, T) be the equicontinuous minimal transformation group with X = pi(infinity)Z(2), the Cantor group, and S = [unk](infinity)Z(2) endowed with the discrete topology acting on X by right multiplication. For any countable group T we construct a function F:X x S --> T such that if (Y, T) is a minimal transformation group, then (X x Y, S) is a minimal transformation group with the action defined by (x, y)s = [xs, yF(x, s)]. If (W, T) is a minimal transformation group and varphi:(Y, T) --> (W, T) is a homomorphism, then identity x varphi:(X x Y, S) --> (X x W, S) is a homomorphism and has many of the same properties that varphi has. For this reason, one may assume that the phase group is abelian (or S) without loss of generality for many relativized problems in topological dynamics.
Tensor network states and algorithms in the presence of a global SU(2) symmetry

NASA Astrophysics Data System (ADS)

Singh, Sukhwinder; Vidal, Guifre

2012-11-01

The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g., with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely, (i) [Singh, Pfeifer, and Vidal, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.050301 82, 050301 (2010)] and (ii) [Singh, Pfeifer, and Vidal, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.115125 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible, and multiplicity free, acting as a global internal symmetry. Then, in (ii) we described the implementation of Abelian group symmetries in much more detail, considering a U(1) symmetry (e.g., conservation of global particle number) as a concrete example. In this paper, we describe the implementation of non-Abelian group symmetries in great detail. For concreteness, we consider an SU(2) symmetry (e.g., conservation of global quantum spin). Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we describe the SU(2)-invariant version of the multiscale entanglement renormalization ansatz and apply it to study the low-energy spectrum of a quantum spin chain with a global SU(2) symmetry.
Instantons, quivers and noncommutative Donaldson-Thomas theory

NASA Astrophysics Data System (ADS)

Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

2011-12-01

We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Hamiltonian Anomalies from Extended Field Theories

NASA Astrophysics Data System (ADS)

Monnier, Samuel

2015-09-01

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.
Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less
Scattering amplitudes in $$\\mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity

DOE PAGES

Chiodaroli, Marco; Gunaydin, Murat; Johansson, Henrik; ...

2015-01-15

We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N = 2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N = 2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian andmore » Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at treelevel and one loop. Lastly, the double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.« less
Phase Transitions in Definite Total Spin States of Two-Component Fermi Gases.

PubMed

Yurovsky, Vladimir A

2017-05-19

Second-order phase transitions have no latent heat and are characterized by a change in symmetry. In addition to the conventional symmetric and antisymmetric states under permutations of bosons and fermions, mathematical group-representation theory allows for non-Abelian permutation symmetry. Such symmetry can be hidden in states with defined total spins of spinor gases, which can be formed in optical cavities. The present work shows that the symmetry reveals itself in spin-independent or coordinate-independent properties of these gases, namely as non-Abelian entropy in thermodynamic properties. In weakly interacting Fermi gases, two phases appear associated with fermionic and non-Abelian symmetry under permutations of particle states, respectively. The second-order transitions between the phases are characterized by discontinuities in specific heat. Unlike other phase transitions, the present ones are not caused by interactions and can appear even in ideal gases. Similar effects in Bose gases and strong interactions are discussed.
On the Grothendieck rings of equivariant fusion categories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burciu, Sebastian, E-mail: sebastian.burciu@imar.ro

2015-07-15

In this paper, we describe a Mackey type decomposition for group actions on abelian categories. This allows us to define new Mackey functors which associates to any subgroup the K-theory of the corresponding equivariantized abelian category. In the case of an action by tensor autoequivalences, the Mackey functor at the level of Grothendieck rings has a Green functor structure. As an application we give a description of the Grothendieck rings of equivariantized fusion categories under group actions by tensor autoequivalences on graded fusion categories. In this settings, a new formula for the tensor product of any two simple objects ofmore » an equivariantized fusion category is given, simplifying the fusion formula from Burciu and Natale [J. Math. Phys. 54, 013511 (2013)].« less
Non-Abelian fractional topological insulators in three spatial dimensions from coupled wires

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher

The study of topological order in three spatial dimensions constitutes a major frontier in theoretical condensed matter physics. Recently, substantial progress has been made in constructing (3+1)-dimensional Abelian topological states of matter from arrays of coupled quantum wires. In this talk, I will illustrate how wire constructions based on non-Abelian bosonization can be used to build and characterize non-Abelian symmetry-enriched topological phases in three dimensions. In particular, I will describe a family of states of matter, constructed in this way, that constitute a natural non-Abelian generalization of strongly correlated three dimensional fractional topological insulators. These states of matter support strongly interacting symmetry-protected gapless surface states, and host non-Abelian pointlike and linelike excitations in the bulk.
When Abelian = Hausdorff

ERIC Educational Resources Information Center

Kohl, Timothy

2012-01-01

A pair of elementary exercises, one from topology, the other from group theory are such that if one replaces three words in the topology problem, you get the group theory problem and vice-versa. This suggests connections between the two that are explored here.
Comment on 'Noncommutative gauge theories and Lorentz symmetry'

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iorio, Alfredo

2008-02-15

We show that Lorentz symmetry is generally absent for noncommutative (Abelian) gauge theories and obtain a compact formula for the divergence of the Noether currents that allows a thorough study of this instance of symmetry violation. We use that formula to explain why the results of ''Noncommutative gauge theories and Lorentz symmetry'', Phys. Rev. D 70, 125004 (2004) by R. Banerjee, B. Chakraborty, and K. Kumar, interpreted there as new criteria for Lorentz invariance, are in fact just a particular case of the general expression for Lorentz violation obtained here. Finally, it is suggested that the divergence formula should holdmore » in a vast class of cases, such as, for instance, the standard model extension.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Bunster, Claudio; Max-Planck-Institut fuer Gravitationsphysik; Henneaux, Marc

There exists a formulation of the Maxwell theory in terms of two vector potentials, one electric and one magnetic. The action is then manifestly invariant under electric-magnetic duality transformations, which are rotations in the two-dimensional internal space of the two potentials, and local. We ask the question: Can duality be gauged? The only known and battle-tested method of accomplishing the gauging is the Noether procedure. In its decanted form, it amounts to turning on the coupling by deforming the Abelian gauge group of the free theory, out of whose curvatures the action is built, into a non-Abelian group which becomesmore » the gauge group of the resulting theory. In this article, we show that the method cannot be successfully implemented for electric-magnetic duality. We thus conclude that, unless a radically new idea is introduced, electric-magnetic duality cannot be gauged. The implication of this result for supergravity is briefly discussed.« less

Global charges of stationary non-Abelian black holes.

PubMed

Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco

2003-05-02

We consider stationary axially symmetric black holes in SU(2) Einstein-Yang-Mills-dilaton theory. We present a mass formula for these stationary non-Abelian black holes, which also holds for Abelian black holes. The presence of the dilaton field allows for rotating black holes, which possess nontrivial electric and magnetic gauge fields, but do not carry a non-Abelian charge. We further present a new uniqueness conjecture.
Collision dynamics of two-dimensional non-Abelian vortices

NASA Astrophysics Data System (ADS)

Mawson, Thomas; Petersen, Timothy C.; Simula, Tapio

2017-09-01

We study computationally the collision dynamics of vortices in a two-dimensional spin-2 Bose-Einstein condensate. In contrast to Abelian vortex pairs, which annihilate or pass through each other, we observe non-Abelian vortex pairs to undergo rungihilation—an event that converts the colliding vortices into a rung vortex. The resulting rung defect subsequently decays to another pair of non-Abelian vortices of different type, accompanied by a magnetization reversal.
Origin of Abelian gauge symmetries in heterotic/F-theory duality

DOE PAGES

Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; ...

2016-04-07

Here, we study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, and also derive both the Calabi-Yau geometry and the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in theirmore » low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) x Z_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. And while the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stuckelberg mechanism in the lower-dimensional effective theory. Finally, in geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.« less
Feynman rules for a whole Abelian model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chauca, J.; Doria, R.; Soares, W.

2012-09-24

Feynman rules for an abelian extension of gauge theories are discussed and explicitly derived. Vertices with three and four abelian gauge bosons are obtained. A discussion on an eventual structure for the photon is presented.
Towards a realization of the condensed-matter-gravity correspondence in string theory via consistent Abelian truncation of the Aharony-Bergman-Jafferis-Maldacena model.

PubMed

Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu

2012-11-02

We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
Metal-Insulator Transition Revisited for Cold Atoms in Non-Abelian Gauge Potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Satija, Indubala I.; National Institute of Standards and Technology, Gaithersburg, Maryland 20899; Dakin, Daniel C.

2006-11-24

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case includemore » the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.« less
On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.
Penrose limits of Abelian and non-Abelian T-duals of AdS 5 × S 5 and their field theory duals

NASA Astrophysics Data System (ADS)

Itsios, Georgios; Nastase, Horatiu; Núñez, Carlos; Sfetsos, Konstantinos; Zacarías, Salomón

2018-01-01

We consider the backgrounds obtained by Abelian and non-Abelian T-duality applied on AdS 5 × S 5. We study geodesics, calculate Penrose limits and find the associated plane-wave geometries. We quantise the weakly coupled type-IIA string theory on these backgrounds. We study the BMN sector, finding operators that wrap the original quiver CFT. For the non-Abelian plane wave, we find a `flow' in the frequencies. We report some progress to understand this, in terms of deconstruction of a higher dimensional field theory. We explore a relation with the plane-wave limit of the Janus solution, which we also provide.
Representation of complex probabilities and complex Gibbs sampling

NASA Astrophysics Data System (ADS)

Salcedo, Lorenzo Luis

2018-03-01

Complex weights appear in Physics which are beyond a straightforward importance sampling treatment, as required in Monte Carlo calculations. This is the wellknown sign problem. The complex Langevin approach amounts to effectively construct a positive distribution on the complexified manifold reproducing the expectation values of the observables through their analytical extension. Here we discuss the direct construction of such positive distributions paying attention to their localization on the complexified manifold. Explicit localized representations are obtained for complex probabilities defined on Abelian and non Abelian groups. The viability and performance of a complex version of the heat bath method, based on such representations, is analyzed.
Dark gauge bosons: LHC signatures of non-abelian kinetic mixing

DOE PAGES

Argüelles, Carlos A.; He, Xiao-Gang; Ovanesyan, Grigory; ...

2017-04-20

We consider non-abelian kinetic mixing between the Standard Model and a dark sector gauge group associated with the presence of a scalar triplet. The magnitude of the resulting dark photon coupling ϵ is determined by the ratio of the triplet vacuum expectation value, constrained to by by electroweak precision tests, to the scale Λ of the effective theory. The corresponding effective operator Wilson coefficient can be while accommodating null results for dark photon searches, allowing for a distinctive LHC dark photon phenomenology. After outlining the possible LHC signatures, we illustrate by recasting current ATLAS dark photon results into the non-abelianmore » mixing context.« less
Fresh look at the Abelian and non-Abelian Landau-Khalatnikov-Fradkin transformations

NASA Astrophysics Data System (ADS)

De Meerleer, T.; Dudal, D.; Sorella, S. P.; Dall'Olio, P.; Bashir, A.

2018-04-01

The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow one to interpolate n -point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our setup is guaranteed to all orders. We also offer a direct path integral derivation in the non-Abelian case, finding full consistency.
Non-Abelian S =1 chiral spin liquid on the kagome lattice

NASA Astrophysics Data System (ADS)

Liu, Zheng-Xin; Tu, Hong-Hao; Wu, Ying-Hai; He, Rong-Qiang; Liu, Xiong-Jun; Zhou, Yi; Ng, Tai-Kai

2018-05-01

We study S =1 spin liquid states on the kagome lattice constructed by Gutzwiller-projected px+i py superconductors. We show that the obtained spin liquids are either non-Abelian or Abelian topological phases, depending on the topology of the fermionic mean-field state. By calculating the modular matrices S and T , we confirm that projected topological superconductors are non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin Hall conductance we obtained agree very well with the S O (3) 1 (or, equivalently, S U (2) 2 ) field-theory predictions. We propose a local Hamiltonian which may stabilize the NACSL. From a variational study, we observe a topological phase transition from the NACSL to the Z2 Abelian spin liquid.
Non-Abelian gauge preheating

NASA Astrophysics Data System (ADS)

Adshead, Peter; Giblin, John T.; Weiner, Zachary J.

2017-12-01

We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian S U (2 ) gauge field. In particular, we examine m2ϕ2 inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.
Gauge backgrounds and zero-mode counting in F-theory

NASA Astrophysics Data System (ADS)

Bies, Martin; Mayrhofer, Christoph; Weigand, Timo

2017-11-01

Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.
A note on local BRST cohomology of Yang-Mills type theories with free Abelian factors

NASA Astrophysics Data System (ADS)

Barnich, Glenn; Boulanger, Nicolas

2018-05-01

We extend previous work on antifield dependent local Becchi-Rouet-Stora-Tyutin (BRST) cohomology for matter coupled gauge theories of Yang-Mills type to the case of gauge groups that involve free Abelian factors. More precisely, we first investigate in a model independent way how the dynamics enters the computation of the cohomology for a general class of Lagrangians in general spacetime dimensions. We then discuss explicit solutions in the case of specific models. Our analysis has implications for the structure of characteristic cohomology and for consistent deformations of the classical models, as well as for divergences/counterterms and for gauge anomalies that may appear during perturbative quantization.
Path-integral invariants in abelian Chern-Simons theory

NASA Astrophysics Data System (ADS)

Guadagnini, E.; Thuillier, F.

2014-05-01

We consider the U(1) Chern-Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.
Zero modes of the non-relativistic self-dual Chern-Simons vortices on the Toda backgrounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Yongsung

The two-dimensional self-dual equations are the governing equations of the static zero-energy vortex solutions for the non-relativistic, non-Abelian Chern-Simons models. The zero modes of the non-relativistic vortices are examined by index calculation for the self-dual equations. The index for the self-dual equations is zero for non-Abelian groups, but a non-zero index is obtained by the Toda Ansatz which reduces the self-dual equations to the Toda equations. The number of zero modes for the non-relativistic Toda vortices is 2 {Sigma}{sub {alpha},{beta}}{sup r}K{sub {alpha}{beta}}Q{sup {beta}} which is twice the total number of isolated zeros of the vortex functions. For the affine Todamore » system, there are additional adjoint zero modes which give a zero index for the SU(N) group.« less
Abelian non-global logarithms from soft gluon clustering

NASA Astrophysics Data System (ADS)

Kelley, Randall; Walsh, Jonathan R.; Zuberi, Saba

2012-09-01

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to previously identified correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections, which are known as clustering logarithms. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution. Using the framework of Soft Collinear Effective Theory (SCET), we show that new clustering effects contributing at NLL arise at each order. While numerical resummation of clustering logs is possible, it is unlikely that they can be analytically resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at O ( {α_s^2} ) for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that clustering logarithms can be naturally thought of as a class of non-global logarithms, which have traditionally been tied to non-Abelian correlations in soft gluon emission.
Conformal field theory construction for non-Abelian hierarchy wave functions

NASA Astrophysics Data System (ADS)

Tournois, Yoran; Hermanns, Maria

2017-12-01

The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
Lattice spin models for non-Abelian chiral spin liquids

DOE PAGES

Lecheminant, P.; Tsvelik, A. M.

2017-04-26

Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2) n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2) n gapless edge excitations.

Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

NASA Astrophysics Data System (ADS)

Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.
Time-reversal-based SU(2) x Sn scalar invariants as (Lie Algebraic) group measures: a structured overview of generalised democratic-recoupled, uniform non-Abelian [AX]n NMR spin systems, as abstract [Formula: see text] chain networks.

PubMed

Temme, F P

2004-03-01

The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2n [AX](2n) spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The [Formula: see text] values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [AX]n model spin systems, including the [AX]3 bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of /SI/=15 (implied by Corio's [Formula: see text] approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper [Formula: see text] network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still higher, 2n-fold regular uniform spin ensemble exhibits a topological FG duality to some known modest /SI/(2i<2n) cardinality--in principle providing for the (sparce) existence of other /SI/(2n) DR-based values.
Non-Abelian holonomies, charge pumping, and quantum computation with Josephson junctions.

PubMed

Faoro, Lara; Siewert, Jens; Fazio, Rosario

2003-01-17

Non-Abelian holonomies can be generated and detected in certain superconducting nanocircuits. Here we consider an example where the non-Abelian operations are related to the adiabatic charge dynamics of the Josephson network. We demonstrate that such a device can be applied both for adiabatic charge pumping and as an implementation of a quantum computer.
New scheme for color confinement and violation of the non-Abelian Bianchi identities

NASA Astrophysics Data System (ADS)

Suzuki, Tsuneo; Ishiguro, Katsuya; Bornyakov, Vitaly

2018-02-01

A new scheme for color confinement in QCD due to violation of the non-Abelian Bianchi identities is proposed. The violation of the non-Abelian Bianchi identities (VNABI) Jμ is equal to Abelian-like monopole currents kμ defined by the violation of the Abelian-like Bianchi identities. Although VNABI is an adjoint operator satisfying the covariant conservation law DμJμ=0 , it satisfies, at the same time, the Abelian-like conservation law ∂μJμ=0 . The Abelian-like conservation law ∂μJμ=0 is also gauge-covariant. There are N2-1 conserved magnetic charges in the case of color S U (N ). The charge of each component of VNABI is quantized à la Dirac. The color-invariant eigenvalues λμ of VNABI also satisfy the Abelian conservation law ∂μλμ=0 and the magnetic charges of the eigenvalues are also quantized à la Dirac. If the color invariant eigenvalues condense in the QCD vacuum, each color component of the non-Abelian electric field Ea is squeezed by the corresponding color component of the solenoidal current Jμa. Then only the color singlets alone can survive as a physical state and non-Abelian color confinement is realized. This confinement picture is completely new in comparison with the previously studied monopole confinement scenario based on an Abelian projection after some partial gauge-fixing, where Abelian neutral states can survive as physical. To check if the scenario is realized in nature, numerical studies are done in the framework of lattice field theory by adopting pure S U (2 ) gauge theory for simplicity. Considering Jμ(x )=kμ(x ) in the continuum formulation, we adopt an Abelian-like definition of a monopole following DeGrand-Toussaint as a lattice version of VNABI, since the Dirac quantization condition of the magnetic charge is satisfied on lattice partially. To reduce severe lattice artifacts, we introduce various techniques of smoothing the thermalized vacuum. Smooth gauge fixings such as the maximal center gauge (MCG), block-spin transformations of Abelian-like monopoles and extraction of physically important infrared long monopole loops are adopted. We also employ the tree-level tadpole improved gauge action of S U (2 ) gluodynamics. With these various improvements, we measure the density of lattice VNABI: ρ (a (β ),n )=∑ μ ,sn √{∑ a (kμa(sn))2 }/(4 √{3 }Vnb3) , where kμa(sn) is an n blocked monopole in the color direction a , n is the number of blocking steps, Vn=V /n4 (b =n a (β )) is the lattice volume (spacing) of the blocked lattice. Beautiful and convincing scaling behaviors are seen when we plot the density ρ (a (β ),n ) versus b =n a (β ). A single universal curve ρ (b ) is found from n =1 to n =12 , which suggests that ρ (a (β ),n ) is a function of b =n a (β ) alone. The universal curve seems independent of a gauge fixing procedure used to smooth the lattice vacuum since the scaling is obtained in all gauges adopted. The scaling, if it exists also for n →∞ , shows that the lattice definition of VNABI has the continuum limit and the new confinement scenario is realized.
Experimental realization of non-Abelian non-adiabatic geometric gates.

PubMed

Abdumalikov, A A; Fink, J M; Juliusson, K; Pechal, M; Berger, S; Wallraff, A; Filipp, S

2013-04-25

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.
Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

NASA Astrophysics Data System (ADS)

Gattringer, Christof; Göschl, Daniel; Marchis, Carlotta

2018-03-01

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.
Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene.

PubMed

Wu, Ying-Hai; Shi, Tao; Jain, Jainendra K

2017-08-09

The current proposals for producing non-Abelian anyons and Majorana particles, which are neither fermions nor bosons, are primarily based on the realization of topological superconductivity in two dimensions. We show theoretically that the unique Landau level structure of bilayer graphene provides a new possible avenue for achieving such exotic particles. Specifically, we demonstrate the feasibility of a "parton" fractional quantum Hall (FQH) state, which supports non-Abelian particles without the usual topological superconductivity. Furthermore, we advance this state as the fundamental explanation of the puzzling 1/2 FQH effect observed in bilayer graphene [ Kim et al. Nano Lett. 2015 , 15 , 7445 ] and predict that it will also occur in trilayer graphene. We indicate experimental signatures that differentiate the parton state from other candidate non-Abelian FQH states and predict that a transverse electric field can induce a topological quantum phase transition between two distinct non-Abelian FQH states.
Dirichlet to Neumann operator for Abelian Yang-Mills gauge fields

NASA Astrophysics Data System (ADS)

Díaz-Marín, Homero G.

We consider the Dirichlet to Neumann operator for Abelian Yang-Mills boundary conditions. The aim is constructing a complex structure for the symplectic space of boundary conditions of Euler-Lagrange solutions modulo gauge for space-time manifolds with smooth boundary. Thus we prepare a suitable scenario for geometric quantization within the reduced symplectic space of boundary conditions of Abelian gauge fields.
Condensation of an ideal gas obeying non-Abelian statistics.

PubMed

Mirza, Behrouz; Mohammadzadeh, Hosein

2011-09-01

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.
Unveiling a spinor field classification with non-Abelian gauge symmetries

NASA Astrophysics Data System (ADS)

Fabbri, Luca; da Rocha, Roldão

2018-05-01

A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this general classification. The Lounesto's classification of spinors is shown to arise as a Pauli's singlet, into this more general classification.
Three dimensional canonical singularity and five dimensional N = 1 SCFT

NASA Astrophysics Data System (ADS)

Xie, Dan; Yau, Shing-Tung

2017-06-01

We conjecture that every three dimensional canonical singularity defines a five dimensional N = 1 SCFT. Flavor symmetry can be found from singularity structure: non-abelian flavor symmetry is read from the singularity type over one dimensional singular locus. The dimension of Coulomb branch is given by the number of compact crepant divisors from a crepant resolution of singularity. The detailed structure of Coulomb branch is described as follows: a) a chamber of Coulomb branch is described by a crepant resolution, and this chamber is given by its Nef cone and the prepotential is computed from triple intersection numbers; b) Crepant resolution is not unique and different resolutions are related by flops; Nef cones from crepant resolutions form a fan which is claimed to be the full Coulomb branch.
On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices

NASA Astrophysics Data System (ADS)

Red'Kov, Victor M.; Bogush, Andrei A.; Tokarevskaya, Natalia G.

2008-02-01

Parametrization of 4 × 4-matrices G of the complex linear group GL(4,C) in terms of four complex 4-vector parameters (k,m,n,l) is investigated. Additional restrictions separating some subgroups of GL(4,C) are given explicitly. In the given parametrization, the problem of inverting any 4 × 4 matrix G is solved. Expression for determinant of any matrix G is found: det G = F(k,m,n,l). Unitarity conditions G+ = G-1 have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups G1, G2, G3 - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consis! ting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators Λk, being of Gell-Mann type, substantially differs from the basis λi used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of GL(4,C) can be used {Λk} = {μiÅνjÅ(μiVνj = KÅL ÅM )}, which permit to factorize SU(4) transformations according to S = eiaμ eibνeikKeilLeimM, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups. Besides, the structure of fifteen Dirac matrices Λk permits to separate twenty 3-parametric subgroups in SU(4) isomorphic to SU(2); those subgroups might be used as bigger elementary blocks in constructing of a general transformation SU(4). It is shown how one can specify the present approach for the pseudounitary group SU(2,2) and SU(3,1).
Electric-magnetic dualities in non-abelian and non-commutative gauge theories

NASA Astrophysics Data System (ADS)

Ho, Jun-Kai; Ma, Chen-Te

2016-08-01

Electric-magnetic dualities are equivalence between strong and weak coupling constants. A standard example is the exchange of electric and magnetic fields in an abelian gauge theory. We show three methods to perform electric-magnetic dualities in the case of the non-commutative U (1) gauge theory. The first method is to use covariant field strengths to be the electric and magnetic fields. We find an invariant form of an equation of motion after performing the electric-magnetic duality. The second method is to use the Seiberg-Witten map to rewrite the non-commutative U (1) gauge theory in terms of abelian field strength. The third method is to use the large Neveu Schwarz-Neveu Schwarz (NS-NS) background limit (non-commutativity parameter only has one degree of freedom) to consider the non-commutative U (1) gauge theory or D3-brane. In this limit, we introduce or dualize a new one-form gauge potential to get a D3-brane in a large Ramond-Ramond (R-R) background via field redefinition. We also use perturbation to study the equivalence between two D3-brane theories. Comparison of these methods in the non-commutative U (1) gauge theory gives different physical implications. The comparison reflects the differences between the non-abelian and non-commutative gauge theories in the electric-magnetic dualities. For a complete study, we also extend our studies to the simplest abelian and non-abelian p-form gauge theories, and a non-commutative theory with the non-abelian structure.
A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer.

PubMed

Sharma, Sandeep

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10(12) many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a(3)Πu, b(3)Σg (-), A(1)Πu, c(3)Σu (+), B(1)Δg, B(') (1)Σg (+), d(3)Πg, and C(1)Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations (1)Σg (+), (1)Σu (+), (1)Σg (-), and (1)Σu (-), to an estimated accuracy of 0.1 mEh of the exact result in this basis.
A general non-Abelian density matrix renormalization group algorithm with application to the C2 dimer

NASA Astrophysics Data System (ADS)

Sharma, Sandeep

2015-01-01

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.
Generalized graph states based on Hadamard matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cui, Shawn X.; Yu, Nengkun; Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1

2015-07-15

Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structure related to a certain graph, which is given by either a stabilizer group or an encoding circuit, both can be directly given by the graph. To generalize graph states, whose stabilizer groups are abelian subgroups of the Pauli group, one approach taken is to study non-abelian stabilizers. In this work, we propose to generalize graph states based on the encoding circuit, which is completely determined by the graph and a Hadamard matrix. We study themore » entanglement structures of these generalized graph states and show that they are all maximally mixed locally. We also explore the relationship between the equivalence of Hadamard matrices and local equivalence of the corresponding generalized graph states. This leads to a natural generalization of the Pauli (X, Z) pairs, which characterizes the local symmetries of these generalized graph states. Our approach is also naturally generalized to construct graph quantum codes which are beyond stabilizer codes.« less
Anyonic braiding in optical lattices

PubMed Central

Zhang, Chuanwei; Scarola, V. W.; Tewari, Sumanta; Das Sarma, S.

2007-01-01

Topological quantum states of matter, both Abelian and non-Abelian, are characterized by excitations whose wavefunctions undergo nontrivial statistical transformations as one excitation is moved (braided) around another. Topological quantum computation proposes to use the topological protection and the braiding statistics of a non-Abelian topological state to perform quantum computation. The enormous technological prospect of topological quantum computation provides new motivation for experimentally observing a topological state. Here, we explicitly work out a realistic experimental scheme to create and braid the Abelian topological excitations in the Kitaev model built on a tunable robust system, a cold atom optical lattice. We also demonstrate how to detect the key feature of these excitations: their braiding statistics. Observation of this statistics would directly establish the existence of anyons, quantum particles that are neither fermions nor bosons. In addition to establishing topological matter, the experimental scheme we develop here can also be adapted to a non-Abelian topological state, supported by the same Kitaev model but in a different parameter regime, to eventually build topologically protected quantum gates. PMID:18000038
New color-magnetic defects in dense quark matter

NASA Astrophysics Data System (ADS)

Haber, Alexander; Schmitt, Andreas

2018-06-01

Color-flavor locked (CFL) quark matter expels color-magnetic fields due to the Meissner effect. One of these fields carries an admixture of the ordinary abelian magnetic field and therefore flux tubes may form if CFL matter is exposed to a magnetic field, possibly in the interior of neutron stars or in quark stars. We employ a Ginzburg–Landau approach for three massless quark flavors, which takes into account the multi-component nature of color superconductivity. Based on the weak-coupling expressions for the Ginzburg–Landau parameters, we identify the regime where CFL is a type-II color superconductor and compute the radial profiles of different color-magnetic flux tubes. Among the configurations without baryon circulation we find a new solution that is energetically preferred over the flux tubes previously discussed in the literature in the parameter regime relevant for compact stars. Within the same setup, we also find a new defect in the 2SC phase, namely magnetic domain walls, which emerge naturally from the previously studied flux tubes if a more general ansatz for the order parameter is used. Color-magnetic defects in the interior of compact stars allow for sustained deformations of the star, potentially strong enough to produce detectable gravitational waves.
Interaction of non-Abelian tensor gauge fields

NASA Astrophysics Data System (ADS)

Savvidy, George

2018-01-01

The non-Abelian tensor gauge fields take value in extended Poincaré algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended Poincaré algebra and through the path integral over the auxiliary vector field with the U(1) Abelian action. We demonstrate that this allows to fix the unitary gauge and derive scattering amplitudes in spinor representation.
About crystal lattices and quasilattices in Euclidean space

NASA Astrophysics Data System (ADS)

Prokhoda, A. S.

2017-07-01

Definitions are given, based on which algorithms have been developed for constructing computer models of two-dimensional quasilattices and the corresponding quasiperiodic tilings in plane, the point symmetry groups of which are dihedral groups D m ( m = 5, 7, 8, 9, 10, 12, 14, 18), and the translation subgroups are free Abelian groups of the fourth or sixth rank. The angles at the tile vertices in the constructed tilings are calculated.

Critical string from non-Abelian vortex in four dimensions

DOE PAGES

Shifman, M.; Yung, A.

2015-09-25

In a class of non-Abelian solitonic vortex strings supported in certain N = 2 super-Yang–Mills theories we search for the vortex which can behave as a critical fundamental string. We use the Polchinski–Strominger criterion of the ultraviolet completeness. We identify an appropriate four-dimensional bulk theory: it has the U(2) gauge group, the Fayet–Iliopoulos term and four flavor hypermultiplets. It supports semilocal vortices with the world-sheet theory for orientational (size) moduli described by the weighted CP(2,2) model. The latter is superconformal. Its target space is six-dimensional. The overall Virasoro central charge is critical. Lastly, we show that the world-sheet theory onmore » the vortex supported in this bulk model is the bona fide critical string.« less
A non-perturbative argument for the non-abelian Higgs mechanism

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Palma, G.; INFN, Sezione di Pisa, Pisa; Strocchi, F., E-mail: franco.strocchi@sns.it

2013-09-15

The evasion of massless Goldstone bosons by the non-abelian Higgs mechanism is proved by a non-perturbative argument in the local BRST gauge. -- Highlights: •The perturbative explanation of the Higgs mechanism (HM) is not under mathematical control. •We offer a non-perturbative proof of the absence of Goldstone bosons from the non-abelian HM. •Our non-perturbative proof in the BRST gauge avoids a mean field ansatz and expansion.
Non-Abelian Berry phase, instantons, and N=(0,4) supersymmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laia, Joao N.

2010-12-15

In supersymmetric quantum mechanics, the non-Abelian Berry phase is known to obey certain differential equations. Here we study N=(0,4) systems and show that the non-Abelian Berry connection over R{sup 4n} satisfies a generalization of the self-dual Yang-Mills equations. Upon dimensional reduction, these become the tt* equations. We further study the Berry connection in N=(4,4) theories and show that the curvature is covariantly constant.
Fault-tolerant Greenberger-Horne-Zeilinger paradox based on non-Abelian anyons.

PubMed

Deng, Dong-Ling; Wu, Chunfeng; Chen, Jing-Ling; Oh, C H

2010-08-06

We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.
Time-reversal-based SU(2)× Sn scalar invariants as (Lie Algebraic) group measures: a structured overview of generalised democratic-recoupled, uniform non-Abelian [ AX] n NMR spin systems, as abstract Sn⊃ Sn-1../U n⊃U n-1.. chain networks

NASA Astrophysics Data System (ADS)

Temme, F. P.

2004-03-01

The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2 n [ AX] 2 n spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The |D 0( U)|((⊗SU(2)) (2n))|SI| values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [ AX] n model spin systems, including the [ AX] 3bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of | SI|=15 (implied by Corio's | D0|((⊗ SU(2)) 2 n) approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper S2n network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still higher, 2 n-fold regular uniform spin ensemble exhibits a topological FG duality to some known modest | SI| (2 i<2 n) cardinality—in principle providing for the (sparce) existence of other | SI| (2 n) DR-based values.
Topological defects in the Georgi-Machacek model

NASA Astrophysics Data System (ADS)

Chatterjee, Chandrasekar; Kurachi, Masafumi; Nitta, Muneto

2018-06-01

We study topological defects in the Georgi-Machacek model in a hierarchical symmetry breaking in which extra triplets acquire vacuum expectation values before the doublet. We find a possibility of topologically stable non-Abelian domain walls and non-Abelian flux tubes (vortices or cosmic strings) in this model. In the limit of the vanishing U (1 )Y gauge coupling in which the custodial symmetry becomes exact, the presence of a vortex spontaneously breaks the custodial symmetry, giving rise to S2 Nambu-Goldstone (NG) modes localized around the vortex corresponding to non-Abelian fluxes. Vortices are continuously degenerated by these degrees of freedom, thereby called non-Abelian. By taking into account the U (1 )Y gauge coupling, the custodial symmetry is explicitly broken, the NG modes are lifted to become pseudo-NG modes, and all non-Abelian vortices fall into a topologically stable Z string. This is in contrast to the standard model in which Z strings are nontopological and are unstable in the realistic parameter region. Non-Abelian domain walls also break the custodial symmetry and are accompanied by localized S2 NG modes. Finally, we discuss the existence of domain wall solutions bounded by flux tubes, where their S2 NG modes match. The domain walls may quantum mechanically decay by creating a hole bounded by a flux tube loop, and would be cosmologically safe. Gravitational waves produced from unstable domain walls could be detected by future experiments.
Braiding light quanta

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio

The possibility that anyons -- quantum particles other than fermions or bosons -- can emerge in condensed matter systems has motivated generations of physicists. In addition to being of fundamental scientific importance, so-called non-Abelian anyons are particularly sought-after for potential applications to quantum computing. However, experimental evidence of anyons in electronic systems remains inconclusive. We propose to demonstrate non-Abelian braiding by injecting coherent states of light into ``topological guided modes'' in specially-fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases. We propose an optical interference experiment to probe this non-Abelian braiding directly. T.I. is supported by a National Science Foundation Graduate Research Fellowship under Grant No. DGE-1247312.
On Non-Abelian Extensions of 3-Lie Algebras

NASA Astrophysics Data System (ADS)

Song, Li-Na; Makhlouf, Abdenacer; Tang, Rong

2018-04-01

In this paper, we study non-abelian extensions of 3-Lie algebras through Maurer-Cartan elements. We show that there is a one-to-one correspondence between isomorphism classes of non-abelian extensions of 3-Lie algebras and equivalence classes of Maurer-Cartan elements in a DGLA. The structure of the Leibniz algebra on the space of fundamental objects is also analyzed. Supported by National Natural Science Foundation of China under Grant No. 11471139 and National Natural Science Foundation of Jilin Province under Grant No. 20170101050JC
Conserved quantities in non-Abelian monopole fields

NASA Astrophysics Data System (ADS)

Horváthy, P. A.; Ngome, J.-P.

2009-06-01

Van Holten’s covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopolelike field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere, and Wilczek, a conserved angular momentum is constructed, despite the nonconservation of the electric charge. No Runge-Lenz vector has been found.
Baryonic Force for Accelerated Cosmic Expansion and Generalized U1b Gauge Symmetry in Particle-Cosmology

NASA Astrophysics Data System (ADS)

Khan, Mehbub; Hao, Yun; Hsu, Jong-Ping

2018-01-01

Based on baryon charge conservation and a generalized Yang-Mills symmetry for Abelian (and non-Abelian) groups, we discuss a new baryonic gauge field and its linear potential for two point-like baryon charges. The force between two point-like baryons is repulsive, extremely weak and independent of distance. However, for two extended baryonic systems, we have a dominant linear force α r. Thus, only in the later stage of the cosmic evolution, when two baryonic galaxies are separated by an extremely large distance, the new repulsive baryonic force can overcome the gravitational attractive force. Such a model provides a gauge-field-theoretic understanding of the late-time accelerated cosmic expansion. The baryonic force can be tested by measuring the accelerated Wu-Doppler frequency shifts of supernovae at different distances.
Interpretation for scales of measurement linking with abstract algebra.

PubMed

Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun

2014-01-01

THE STEVENS CLASSIFICATION OF LEVELS OF MEASUREMENT INVOLVES FOUR TYPES OF SCALE: "Nominal", "Ordinal", "Interval" and "Ratio". This classification has been used widely in medical fields and has accomplished an important role in composition and interpretation of scale. With this classification, levels of measurements appear organized and validated. However, a group theory-like systematization beckons as an alternative because of its logical consistency and unexceptional applicability in the natural sciences but which may offer great advantages in clinical medicine. According to this viewpoint, the Stevens classification is reformulated within an abstract algebra-like scheme; 'Abelian modulo additive group' for "Ordinal scale" accompanied with 'zero', 'Abelian additive group' for "Interval scale", and 'field' for "Ratio scale". Furthermore, a vector-like display arranges a mixture of schemes describing the assessment of patient states. With this vector-like notation, data-mining and data-set combination is possible on a higher abstract structure level based upon a hierarchical-cluster form. Using simple examples, we show that operations acting on the corresponding mixed schemes of this display allow for a sophisticated means of classifying, updating, monitoring, and prognosis, where better data mining/data usage and efficacy is expected.
Low-energy effective worldsheet theory of a non-Abelian vortex in high-density QCD revisited: A regular gauge construction

NASA Astrophysics Data System (ADS)

Chatterjee, Chandrasekhar; Nitta, Muneto

2017-04-01

Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the C P2 model [1,2]. Here, we reconstruct the effective theory in a regular gauge without taking a singular gauge, confirming the previous results in the singular gauge. As a byproduct of our analysis, we find that non-Abelian vortices in high-density QCD do not suffer from any obstruction for the global definition of a symmetry breaking.
Non-abelian anyons and topological quantum information processing in 1D wire networks

NASA Astrophysics Data System (ADS)

Alicea, Jason

2012-02-01

Topological quantum computation provides an elegant solution to decoherence, circumventing this infamous problem at the hardware level. The most basic requirement in this approach is the ability to stabilize and manipulate particles exhibiting non-Abelian exchange statistics -- Majorana fermions being the simplest example. Curiously, Majorana fermions have been predicted to arise both in 2D systems, where non-Abelian statistics is well established, and in 1D, where exchange statistics of any type is ill-defined. An important question then arises: do Majorana fermions in 1D hold the same technological promise as their 2D counterparts? In this talk I will answer this question in the affirmative, describing how one can indeed manipulate and harness the non-Abelian statistics of Majoranas in a remarkably simple fashion using networks formed by quantum wires or topological insulator edges.
Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

NASA Astrophysics Data System (ADS)

Mong, Roger S. K.; Clarke, David J.; Alicea, Jason; Lindner, Netanel H.; Fendley, Paul; Nayak, Chetan; Oreg, Yuval; Stern, Ady; Berg, Erez; Shtengel, Kirill; Fisher, Matthew P. A.

2014-01-01

Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from Read and Green's observation that the Moore-Read quantum Hall state and a (relatively simple) two-dimensional p+ip superconductor both support so-called Ising non-Abelian anyons. Here, we establish a similar correspondence between the Z3 Read-Rezayi quantum Hall state and a novel two-dimensional superconductor in which charge-2e Cooper pairs are built from fractionalized quasiparticles. In particular, both phases harbor Fibonacci anyons that—unlike Ising anyons—allow for universal topological quantum computation solely through braiding. Using a variant of Teo and Kane's construction of non-Abelian phases from weakly coupled chains, we provide a blueprint for such a superconductor using Abelian quantum Hall states interlaced with an array of superconducting islands. Fibonacci anyons appear as neutral deconfined particles that lead to a twofold ground-state degeneracy on a torus. In contrast to a p+ip superconductor, vortices do not yield additional particle types, yet depending on nonuniversal energetics can serve as a trap for Fibonacci anyons. These results imply that one can, in principle, combine well-understood and widely available phases of matter to realize non-Abelian anyons with universal braid statistics. Numerous future directions are discussed, including speculations on alternative realizations with fewer experimental requirements.
Semi-abelian Z-theory: NLSM+ ϕ 3 from the open string

NASA Astrophysics Data System (ADS)

Carrasco, John Joseph M.; Mafra, Carlos R.; Schlotterer, Oliver

2017-08-01

We continue our investigation of Z-theory, the second double-copy component of open-string tree-level interactions besides super-Yang-Mills (sYM). We show that the amplitudes of the extended non-linear sigma model (NLSM) recently considered by Cachazo, Cha, and Mizera are reproduced by the leading α '-order of Z-theory amplitudes in the semi-abelian case. The extension refers to a coupling of NLSM pions to bi-adjoint scalars, and the semi-abelian case involves to a partial symmetrization over one of the color orderings that characterize the Z-theory amplitudes. Alternatively, the partial symmetrization corresponds to a mixed interaction among abelian and non-abelian states in the underlying open-superstring amplitude. We simplify these permutation sums via monodromy relations which greatly increase the efficiency in extracting the α '-expansion of these amplitudes. Their α '-corrections encode higher-derivative interactions between NLSM pions and bi-colored scalars all of which obey the duality between color and kinematics. Through double-copy, these results can be used to generate the predictions of supersymmetric Dirac-Born-Infeld-Volkov-Akulov theory coupled with sYM as well as a complete tower of higher-order α '-corrections.
On non-abelian T-duality and deformations of supercoset string sigma-models

NASA Astrophysics Data System (ADS)

Borsato, Riccardo; Wulff, Linus

2017-10-01

We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra \\tilde{g} of the superisometry algebra. These models inherit the classical integrability of the parent one, and they include as special cases the so-called homogeneous Yang-Baxter sigma models as well as their non-abelian T-duals. Many properties of DTD models have simple algebraic interpretations. For example we show that their (non-abelian) T-duals — including certain deformations — are again in the same class, where \\tilde{g} gets enlarged or shrinks by adding or removing generators corresponding to the dualised isometries. Moreover, we show that Weyl invariance of these models is equivalent to \\tilde{g} being unimodular; when this property is not satisfied one can always remove one generator to obtain a unimodular \\tilde{g} , which is equivalent to (formal) T-duality. We also work out the target space superfields and, as a by-product, we prove the conjectured transformation law for Ramond-Ramond (RR) fields under bosonic non-abelian T-duality of supercosets, generalising it to cases involving also fermionic T-dualities.
Topological invariants measured for Abelian and non-Abelian monopole fields

NASA Astrophysics Data System (ADS)

Sugawa, Seiji; Salces Carcoba, Francisco; Perry, Abigail; Yue, Yuchen; Putra, Andika; Spielman, Ian

2016-05-01

Understanding the topological nature of physical systems is an important topic in contemporary physics, ranging from condensed matter to high energy. In this talk, I will present experiments measuring the 1st and 2nd Chern number in a four-level quantum system both with degenerate and non-degenerate energies. We engineered the system's Hamiltonian by coupling hyperfine ground states of rubidium-87 Bose-Einstein condensates with rf and microwave fields. We non-adiabatically drove the system and measured the linear response to obtain the local (non-Abelian) Berry curvatures. Then, the Chern numbers were evaluated on (hyper-)spherical manifolds in parameter space. We obtain Chern numbers close to unity for both the 1st and the 2nd Chern numbers. The non-zero Chern number can be interpreted as monopole residing inside the manifold. For our system, the monopoles correspond to a Dirac monopole for non-degenerate spectra and a Yang monopole for our degenerate case. We also show how the dynamical evolution under non-Abelian gauge field emerged in degenerate quantum system is different from non-degenerate case by showing path-dependent acquisition of non-Abelian geometric phase and Wilson loops.
Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers

NASA Astrophysics Data System (ADS)

Yin, Long-Jing; Qiao, Jia-Bin; Zuo, Wei-Jie; Li, Wen-Tian; He, Lin

2015-08-01

Non-Abelian gauge potentials are quite relevant in subatomic physics, but they are relatively rare in a condensed matter context. Here we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by scanning tunneling microscopy and spectroscopy. At a magic twisted angle, θ ≈(1.11±0.05 ) ∘ , a pronounced sharp peak, which arises from the nondispersive flat bands at the charge neutrality point, is observed in the tunneling density of states due to the action of the non-Abelian gauge fields. Moreover, we observe confined electronic states in the twisted bilayer, as manifested by regularly spaced tunneling peaks with energy spacing δ E ≈vF/D ≈70 meV (here vF is the Fermi velocity of graphene and D is the period of the moiré patterns). This indicates that the non-Abelian gauge potentials in twisted graphene bilayers confine low-energy electrons into a triangular array of quantum dots following the modulation of the moiré patterns. Our results also directly demonstrate that the Fermi velocity in twisted bilayers can be tuned from about 106m /s to zero by simply reducing the twisted angle of about 2∘.
Exact results for the star lattice chiral spin liquid

NASA Astrophysics Data System (ADS)

Kells, G.; Mehta, D.; Slingerland, J. K.; Vala, J.

2010-03-01

We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex-free sector and its time-reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The Abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters between the vertices on triangles are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the threefold non-Abelian ground-state degeneracy on a torus by explicit calculation.
A general non-Abelian density matrix renormalization group algorithm with application to the C{sub 2} dimer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Sandeep, E-mail: sanshar@gmail.com

2015-01-14

We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve ofmore » the C{sub 2} dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 10{sup 12} many-body states. While our calculated energy lies within the 0.3 mE{sub h} error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mE{sub h}, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (T{sub e}) of eight lowest lying excited states: a{sup 3}Π{sub u}, b{sup 3}Σ{sub g}{sup −}, A{sup 1}Π{sub u}, c{sup 3}Σ{sub u}{sup +}, B{sup 1}Δ{sub g}, B{sup ′1}Σ{sub g}{sup +}, d{sup 3}Π{sub g}, and C{sup 1}Π{sub g} are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations {sup 1}Σ{sub g}{sup +}, {sup 1}Σ{sub u}{sup +}, {sup 1}Σ{sub g}{sup −}, and {sup 1}Σ{sub u}{sup −}, to an estimated accuracy of 0.1 mE{sub h} of the exact result in this basis.« less

Condition for confinement in non-Abelian gauge theories

NASA Astrophysics Data System (ADS)

Chaichian, Masud; Frasca, Marco

2018-06-01

We show that a criterion for confinement, based on the BRST invariance, holds in four dimensions, by solving a non-Abelian gauge theory with a set of exact solutions. The confinement condition we consider was obtained by Kugo and Ojima some decades ago. The current understanding of gauge theories permits us to apply the techniques straightforwardly for checking the validity of this criterion. In this way, we are able to show that the non-Abelian gauge theory is confining and that confinement is rooted in the BRST invariance and asymptotic freedom.
Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators.

PubMed

Mross, David F; Essin, Andrew; Alicea, Jason; Stern, Ady

2016-01-22

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of weak topological insulator surfaces manifests itself in a nontrivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap Z_{4} parafermion zero modes.
Spin-adapted matrix product states and operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.
Toward a Parastatistics in Quantum Nonextensive Statistical Mechanics

NASA Astrophysics Data System (ADS)

Zaripov, R. G.

2018-05-01

On the basis of Bose quantum states in parastatistics the equations for the equilibrium distribution of quantum additive and nonextensive systems are determined. The fluctuations and variances of physical quantities for the equilibrium system are found. The Abelian group of microscopic entropies is determined for the composition law with a quadratic nonlinearity.
Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

NASA Astrophysics Data System (ADS)

Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.

2000-11-01

An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
Cogenerating and pre-annihilating dark matter by a new gauge interaction in a unified model

DOE PAGES

Barr, S. M.; Scherrer, Robert J.

2016-05-31

Here, grand unified theories based on large groups (with rank ≥ 6) are a natural context for dark matter models. They contain Standard-Model-singlet fermions that could be dark matter candidates, and can contain new non-abelian interactions whose sphalerons convert baryons, leptons, and dark matter into each other, ''cogenerating" a dark matter asymmetry comparable to the baryon asymmetry. In this paper it is shown that the same non-abelian interactions can ''pre-annihilate" the symmetric component of heavy dark matter particles χ, which then decay late into light stable dark matter particles ζ that inherit their asymmetry. We derive cosmological constraints on themore » parameters of such models. The mass of χ must be < 3000 TeV and their decays must happen when 2 × 10 –7 < T dec/mχ < 10 –4. It is shown that such decays can come from d=5 operators with coefficients of order 1/MGUT or 1/M Pℓ. We present a simple realization of our model based on the group SU(7).« less
Multiflavor string-net models

NASA Astrophysics Data System (ADS)

Lin, Chien-Hung

2017-05-01

We generalize the string-net construction to multiple flavors of strings, each of which is labeled by the elements of an Abelian group Gi. The same flavor of strings can branch, while different flavors of strings can cross one another and thus they form intersecting string nets. We systematically construct the exactly soluble lattice Hamiltonians and the ground-state wave functions for the intersecting string-net condensed phases. We analyze the braiding statistics of the low-energy quasiparticle excitations and find that our model can realize all the topological phases as the string-net model with group G =∏iGi . In this respect, our construction provides various ways of building lattice models which realize topological order G , corresponding to different partitions of G and thus different flavors of string nets. In fact, our construction concretely demonstrates the Künneth formula by constructing various lattice models with the same topological order. As an example, we construct the G =Z2×Z2×Z2 string-net model which realizes a non-Abelian topological phase by properly intersecting three copies of toric codes.
Gauge-invariant variables and entanglement entropy

NASA Astrophysics Data System (ADS)

Agarwal, Abhishek; Karabali, Dimitra; Nair, V. P.

2017-12-01

The entanglement entropy (EE) of gauge theories in three spacetime dimensions is analyzed using manifestly gauge-invariant variables defined directly in the continuum. Specifically, we focus on the Maxwell, Maxwell-Chern-Simons (MCS), and non-Abelian Yang-Mills theories. Special attention is paid to the analysis of edge modes and their contribution to EE. The contact term is derived without invoking the replica method and its physical origin is traced to the phase space volume measure for the edge modes. The topological contribution to the EE for the MCS case is calculated. For all the Abelian cases, the EE presented in this paper agrees with known results in the literature. The EE for the non-Abelian theory is computed in a gauge-invariant Gaussian approximation, which incorporates the dynamically generated mass gap. A formulation of the contact term for the non-Abelian case is also presented.
Gravitational waves from non-Abelian gauge fields at a tachyonic transition

NASA Astrophysics Data System (ADS)

Tranberg, Anders; Tähtinen, Sara; Weir, David J.

2018-04-01

We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.
Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential: Gauge Invariance and Experimental Detections

PubMed Central

Sun, Fadi; Yu, Xiao-Lu; Ye, Jinwu; Fan, Heng; Liu, Wu-Ming

2013-01-01

The method of synthetic gauge potentials opens up a new avenue for our understanding and discovering novel quantum states of matter. We investigate the topological quantum phase transition of Fermi gases trapped in a honeycomb lattice in the presence of a synthetic non-Abelian gauge potential. We develop a systematic fermionic effective field theory to describe a topological quantum phase transition tuned by the non-Abelian gauge potential and explore its various important experimental consequences. Numerical calculations on lattice scales are performed to compare with the results achieved by the fermionic effective field theory. Several possible experimental detection methods of topological quantum phase transition are proposed. In contrast to condensed matter experiments where only gauge invariant quantities can be measured, both gauge invariant and non-gauge invariant quantities can be measured by experimentally generating various non-Abelian gauges corresponding to the same set of Wilson loops. PMID:23846153
Core structure and dynamics of non-Abelian vortices in a biaxial nematic spinor Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Borgh, Magnus O.; Ruostekoski, Janne

2016-05-01

We demonstrate that multiple interaction-dependent defect core structures as well as dynamics of non-Abelian vortices can be realized in the biaxial nematic (BN) phase of a spin-2 atomic Bose-Einstein condensate (BEC). An experimentally simple protocol may be used to break degeneracy with the uniaxial nematic phase. We show that a discrete spin-space symmetry in the core may be reflected in a breaking of its spatial symmetry. The discrete symmetry of the BN order parameter leads to non-commuting vortex charges. We numerically simulate reconnection of non-Abelian vortices, demonstrating formation of the obligatory rung vortex. In addition to atomic BECs, non-Abelian vortices are theorized in, e.g., liquid crystals and cosmic strings. Our results suggest the BN spin-2 BEC as a prime candidate for their realization. We acknowledge financial support from the EPSRC.
Model of chiral spin liquids with Abelian and non-Abelian topological phases

NASA Astrophysics Data System (ADS)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; Tsvelik, A. M.

2017-12-01

We present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, the Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.
Rotation forms and local Hamiltonian monodromy

NASA Astrophysics Data System (ADS)

Efstathiou, K.; Giacobbe, A.; Mardešić, P.; Sugny, D.

2017-02-01

The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach is that the residue-like formula can be shown to be local in a neighborhood of a singularity, hence allowing the definition of monodromy also in the case of non-compact fibers. This idea has been introduced in the literature under the name of scattering monodromy. We prove the coincidence of the two definitions with the monodromy of an appropriately chosen compactification.
Gauge invariance for a whole Abelian model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chauca, J.; Doria, R.; Soares, W.

Light invariance is a fundamental principle for physics be done. It generates Maxwell equations, relativity, Lorentz group. However there is still space for a fourth picture be developed which is to include fields with same Lorentz nature. It brings a new room for field theory. It says that light invariance does not work just to connect space and time but it also associates different fields with same nature. Thus for the ((1/2),(1/2)) representation there is a fields family {l_brace}A{sub {mu}I}{r_brace} to be studied. This means that given such fields association one should derive its corresponding gauge theory. This is themore » effort at this work. Show that there is a whole gauge theory to cover these fields relationships. Considering the abelian case, prove its gauge invariance. It yields the kinetic, massive, trilinear and quadrilinear gauge invariant terms.« less
Ermakov's Superintegrable Toy and Nonlocal Symmetries

NASA Astrophysics Data System (ADS)

Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.

2005-11-01

We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Non-Abelian monopole in the parameter space of point-like interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz

2014-12-15

We study non-Abelian geometric phase in N=2 supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry’s connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule. - Highlights: • Supersymmetric quantum mechanics is an ideal playground for studying geometric phase. • We determine the parameter space of supersymmetric point-like interactions. • Berry’s connection is given by a Wu–Yang-like magnetic monopole in SU(2) Yang–Mills.
Condensation and critical exponents of an ideal non-Abelian gas

NASA Astrophysics Data System (ADS)

Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein

2017-11-01

We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.
String universality in ten dimensions.

PubMed

Adams, Allan; Taylor, Washington; Dewolfe, Oliver

2010-08-13

We show that the N=1 supergravity theories in ten dimensions with gauge groups U(1){496} and E{8}×U(1){248} are not consistent quantum theories. Cancellation of anomalies cannot be made compatible with supersymmetry and Abelian gauge invariance. Thus, in ten dimensions all supersymmetric theories of gravity without known inconsistencies are realized in string theory.
Interacting Non-Abelian Anti-Symmetric Tensor Field Theories

NASA Astrophysics Data System (ADS)

Ekambaram, K.; Vytheeswaran, A. S.

2018-04-01

Non-Abelian Anti-symmetric Tensor fields interacting with vector fields have a complicated constraint structure. We enlarge the gauge invariance in this system. Relevant gauge invariant quantities including the Hamiltonian are obtained. We also make introductory remarks on a different but more complicated gauge theory.
Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE PAGES

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio; ...

2017-12-15

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less

Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Escalante, Alberto, E-mail: aescalan@ifuap.buap.mx; Manuel-Cabrera, J., E-mail: jmanuel@ifuap.buap.mx

2015-10-15

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. - Highlights: • A detailed Faddeev–Jackiw analysis for exotic action of gravity is performed.more » • We show that Dirac’s brackets and Generalized [FJ] brackets are equivalent. • Without fixing the gauge exotic action is a non-commutative theory. • The fundamental gauge transformations of the theory are found. • Dirac and Faddeev–Jackiw approaches are compared.« less
Model of chiral spin liquids with Abelian and non-Abelian topological phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jyong-Hao; Mudry, Christopher; Chamon, Claudio

In this article, we present a two-dimensional lattice model for quantum spin-1/2 for which the low-energy limit is governed by four flavors of strongly interacting Majorana fermions. We study this low-energy effective theory using two alternative approaches. The first consists of a mean-field approximation. The second consists of a random phase approximation (RPA) for the single-particle Green's functions of the Majorana fermions built from their exact forms in a certain one-dimensional limit. The resulting phase diagram consists of two competing chiral phases, one with Abelian and the other with non-Abelian topological order, separated by a continuous phase transition. Remarkably, themore » Majorana fermions propagate in the two-dimensional bulk, as in the Kitaev model for a spin liquid on the honeycomb lattice. We identify the vison fields, which are mobile (they are static in the Kitaev model) domain walls propagating along only one of the two space directions.« less
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

NASA Astrophysics Data System (ADS)

Kholodenko, Arkady L.

2016-08-01

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang-Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric-magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada's results by carefully analyzing and classifying all dynamically generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].
Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.
Four Proofs of the Converse of the Chinese Remainder Theorem

ERIC Educational Resources Information Center

Dobbs, D. E.

2008-01-01

Four proofs, designed for classroom use in varying levels of courses on abstract algebra, are given for the converse of the classical Chinese Remainder Theorem over the integers. In other words, it is proved that if m and n are integers greater than 1 such that the abelian groups [double-struck z][subscript m] [direct sum] [double-struck…
Poisson-Lie duals of the η deformed symmetric space sigma model

NASA Astrophysics Data System (ADS)

Hoare, Ben; Seibold, Fiona K.

2017-11-01

Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G0 is associated to a sub-Dynkin diagram. Additional U1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS5 × S5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.
$$ \\mathcal{N}=1 $$ deformations and RG flows of $$ \\mathcal{N}=2 $$ SCFTs

DOE PAGES

Maruyoshi, Kazunobu; Song, Jaewon

2017-02-14

Here, we study certainmore » $$ \\mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \\mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \\mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \\mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the ( A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \\mathcal{N}=1 $$ fixed points.« less
$$ \\mathcal{N}=1 $$ deformations and RG flows of $$ \\mathcal{N}=2 $$ SCFTs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maruyoshi, Kazunobu; Song, Jaewon

Here, we study certainmore » $$ \\mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \\mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \\mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \\mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the ( A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \\mathcal{N}=1 $$ fixed points.« less
Non-Abelian states of matter.

PubMed

Stern, Ady

2010-03-11

Quantum mechanics classifies all elementary particles as either fermions or bosons, and this classification is crucial to the understanding of a variety of physical systems, such as lasers, metals and superconductors. In certain two-dimensional systems, interactions between electrons or atoms lead to the formation of quasiparticles that break the fermion-boson dichotomy. A particularly interesting alternative is offered by 'non-Abelian' states of matter, in which the presence of quasiparticles makes the ground state degenerate, and interchanges of identical quasiparticles shift the system between different ground states. Present experimental studies attempt to identify non-Abelian states in systems that manifest the fractional quantum Hall effect. If such states can be identified, they may become useful for quantum computation.
Quantization of higher abelian gauge theory in generalized differential cohomology

NASA Astrophysics Data System (ADS)

Szabo, R.

We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
Modified non-Abelian Toda field equations and twisted quasigraded Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skrypnyk, T.

We construct a new family of quasigraded Lie algebras that admit the Kostant-Adler scheme. They coincide with special quasigraded deformations of twisted subalgebras of the loop algebras. Using them we obtain new hierarchies of integrable equations in partial derivatives which we call 'modified' non-Abelian Toda field hierarchies.
Trivial solutions of generalized supergravity vs non-abelian T-duality anomaly

NASA Astrophysics Data System (ADS)

Wulff, Linus

2018-06-01

The equations that follow from kappa symmetry of the type II Green-Schwarz string are a certain deformation, by a Killing vector field K, of the type II supergravity equations. We analyze under what conditions solutions of these 'generalized' supergravity equations are trivial in the sense that they solve also the standard supergravity equations. We argue that for this to happen K must be null and satisfy dK =iK H with H = dB the NSNS three-form field strength. Non-trivial examples are provided by symmetric pp-wave solutions. We then analyze the consequences for non-abelian T-duality and the closely related homogenous Yang-Baxter sigma models. When one performs non-abelian T-duality of a string sigma model on a non-unimodular (sub)algebra one generates a non-vanishing K proportional to the trace of the structure constants. This is expected to lead to an anomaly but we show that when K satisfies the same conditions the anomaly in fact goes away leading to more possibilities for non-anomalous non-abelian T-duality.
Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian geometry

NASA Astrophysics Data System (ADS)

Zanardi, Paolo; Campos Venuti, Lorenzo

2018-01-01

We establish a direct connection between the power of a unitary map in d-dimensions (d < ∞) to generate quantum coherence and the geometry of the set Md of maximally abelian subalgebras (of the quantum system full operator algebra). This set can be seen as a topologically non-trivial subset of the Grassmannian over linear operators. The natural distance over the Grassmannian induces a metric structure on Md, which quantifies the lack of commutativity between the pairs of subalgebras. Given a maximally abelian subalgebra, one can define, on physical grounds, an associated measure of quantum coherence. We show that the average quantum coherence generated by a unitary map acting on a uniform ensemble of quantum states in the algebra (the so-called coherence generating power of the map) is proportional to the distance between a pair of maximally abelian subalgebras in Md connected by the unitary transformation itself. By embedding the Grassmannian into a projective space, one can pull-back the standard Fubini-Study metric on Md and define in this way novel geometrical measures of quantum coherence generating power. We also briefly discuss the associated differential metric structures.
Mapping the Braiding Properties of Non-Abelian FQHE Liquids.

NASA Astrophysics Data System (ADS)

Prodan, Emil; Haldane, F. D. M.

2007-03-01

Non-Abelian FQHE (NAFQHE) states have elementary excitations that cannot be individually locally-created. When widely separated, they give rise to topological (quasi-)degeneracy of the quantum states; braiding of such non-Abelian quasiparticles (NAQP's) implements unitary transformations among the degenerate states that may be useful for ``topological quantum computing'' (TQC). We have developed a new technique for explicit computation of NAQP braiding in models exhibiting ideal NAFQHE behavior (where the topological degeneracy is exact), in particular the Moore-Read ν = 5/2 state. For systems of small numbers of NAQP's on a sphere, we have computed the non-Abelian Berry curvature and Hilbert space metric, as one NAQP is moved relative to a fixed configuration of the others, showing how the topological properties develop as the system size (NAQP separation) increases. We also studied the effect of perturbations (Coulomb interaction and substrate potentials) that lift the exact degeneracy, and become the dominant corrections when NAQP's are brought together so that quantum measurements can be made; these effects are likely to be crucial in determining whether TQC is viable in NAFQHE systems.
Digital lattice gauge theories

NASA Astrophysics Data System (ADS)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

2017-02-01

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
S -duality for holographic p -wave superconductors

NASA Astrophysics Data System (ADS)

Gorsky, Alexander; Gubankova, Elena; Meyer, René; Zayakin, Andrey

2017-11-01

We consider the generalization of the S -duality transformation previously investigated in the context of the fractional quantum Hall effect (FQHE) and s -wave superconductivity to p -wave superconductivity in 2 +1 dimensions in the framework of the AdS /CFT correspondence. The vector Cooper condensate transforms under the S -duality action to the pseudovector condensate at the dual side. The 3 +1 -dimensional Einstein-Yang-Mills theory, the holographic dual to p -wave superconductivity, is used to investigate the S -duality action via the AdS /CFT correspondence. It is shown that, in order to implement the duality transformation, chemical potentials on both the electric and magnetic sides of the duality have to be introduced. A relation for the product of the non-Abelian conductivities in the dual models is derived. We also conjecture a flavor S -duality transformation in the holographic dual to 3 +1 -dimensional QCD low-energy QCD with non-Abelian flavor gauge groups. The conjectured S -duality interchanges isospin and baryonic chemical potentials.
Algebraic cycles and local anomalies in F-theory

NASA Astrophysics Data System (ADS)

Bies, Martin; Mayrhofer, Christoph; Weigand, Timo

2017-11-01

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in six- and four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.
Non-Abelian strategies in quantum penny flip game

NASA Astrophysics Data System (ADS)

Mishima, Hiroaki

2018-01-01

In this paper, we formulate and analyze generalizations of the quantum penny flip game. In the penny flip game, one coin has two states, heads or tails, and two players apply alternating operations on the coin. In the original Meyer game, the first player is allowed to use quantum (i.e., non-commutative) operations, but the second player is still only allowed to use classical (i.e., commutative) operations. In our generalized games, both players are allowed to use non-commutative operations, with the second player being partially restricted in what operators they use. We show that even if the second player is allowed to use "phase-variable" operations, which are non-Abelian in general, the first player still has winning strategies. Furthermore, we show that even when the second player is allowed to choose one from two or more elements of the group U(2), the second player has winning strategies under certain conditions. These results suggest that there is often a method for restoring the quantum state disturbed by another agent.
AGT relations for abelian quiver gauge theories on ALE spaces

NASA Astrophysics Data System (ADS)

Pedrini, Mattia; Sala, Francesco; Szabo, Richard J.

2016-05-01

We construct level one dominant representations of the affine Kac-Moody algebra gl̂k on the equivariant cohomology groups of moduli spaces of rank one framed sheaves on the orbifold compactification of the minimal resolution Xk of the Ak-1 toric singularity C2 /Zk. We show that the direct sum of the fundamental classes of these moduli spaces is a Whittaker vector for gl̂k, which proves the AGT correspondence for pure N = 2 U(1) gauge theory on Xk. We consider Carlsson-Okounkov type Ext-bundles over products of the moduli spaces and use their Euler classes to define vertex operators. Under the decomposition gl̂k ≃ h ⊕sl̂k, these vertex operators decompose as products of bosonic exponentials associated to the Heisenberg algebra h and primary fields of sl̂k. We use these operators to prove the AGT correspondence for N = 2 superconformal abelian quiver gauge theories on Xk.
Thermodynamic properties of Fermi gases in states with defined many-body spins

NASA Astrophysics Data System (ADS)

Yurovsky, Vladimir

2016-05-01

Zero-range interactions in cold spin- 1 / 2 Fermi gases can be described by single interaction strength, since collisions of atoms in the same spin state are forbidden by the Pauli principle. In a spin-independent trap potential (even in the presence of a homogeneous spin-dependent external field), the gas can persist in a state with the given many-body spin, since the spin operator commutes with the Hamiltonian. Spin and spatial degrees of freedom in such systems are separated, and the spin and spatial wavefunctions form non-Abelian irreducible representations of the symmetric group, unless the total spin is S = N / 2 for N atoms (see). Although the total wavefunction, being a linear combination of products of the spin and spatial functions, is permutation-antisymmetric, the non-Abelian permutation symmetry is disclosed in the matrix elements and, as demonstrated here, in thermodynamic properties. The effects include modification of the specific heat and compressibility of the gas.

An efficient matrix product operator representation of the quantum chemical Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch; Dolfi, Michele, E-mail: dolfim@phys.ethz.ch

We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction schememore » presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Kenneth, O., E-mail: kenneth@physics.technion.ac.il; Avron, J.E.

Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with fluxes Φ{sub a}∈R. The positions, r{sub a}∈R{sup 2}, of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls. The holonomies can sometimes be abelian, but in general are not. They can sometimes be topological, but in general are not. We analyse some of the special cases and some of the general ones. Our most interesting results concern themore » cases where holonomy turns out to be topological which is the case when all the fluxons are subcritical, Φ{sub a}<1, and the number of zero modes is D=N−1. If N≥3 it is also non-abelian. In the special case that the fluxons carry identical fluxes the resulting anyons satisfy the Burau representations of the braid group.« less
Optical knots and contact geometry II. From Ranada dyons to transverse and cosmetic knots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kholodenko, Arkady L., E-mail: string@clemson.edu

2016-08-15

Some time ago Ranada (1989) obtained new nontrivial solutions of the Maxwellian gauge fields without sources. These were reinterpreted in Kholodenko (2015) [10] (part I) as particle-like (monopoles, dyons, etc.). They were obtained by the method of Abelian reduction of the non-Abelian Yang–Mills functional. The developed method uses instanton-type calculations normally employed for the non-Abelian gauge fields. By invoking the electric–magnetic duality it then becomes possible to replace all known charges/masses by the particle-like solutions of the source-free Abelian gauge fields. To employ these results in high energy physics, it is essential to extend Ranada’s results by carefully analyzing and classifying all dynamicallymore » generated knotted/linked structures in gauge fields, including those discovered by Ranada. This task is completed in this work. The study is facilitated by the recent progress made in solving the Moffatt conjecture. Its essence is stated as follows: in steady incompressible Euler-type fluids the streamlines could have knots/links of all types. By employing the correspondence between the ideal hydrodynamics and electrodynamics discussed in part I and by superimposing it with the already mentioned method of Abelian reduction, it is demonstrated that in the absence of boundaries only the iterated torus knots and links could be dynamically generated. Obtained results allow to develop further particle-knot/link correspondence studied in Kholodenko (2015) [13].« less
The static quark potential from the gauge independent Abelian decomposition

NASA Astrophysics Data System (ADS)

Cundy, Nigel; Cho, Y. M.; Lee, Weonjong; Leem, Jaehoon

2015-06-01

We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field n; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path-ordered integral of the non-Abelian gauge fields and an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without requiring an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field n winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. Unlike most studies of confinement using the Abelian decomposition, we do not rely on a dual-Meissner effect to create the inter-quark potential. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks of a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects, or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement.
The formation of compact groups of galaxies. I: Optical properties

NASA Technical Reports Server (NTRS)

Diaferio, Antonaldo; Geller, Margaret J.; Ramella, Massimo

1994-01-01

The small crossing time of compact groups of galaxies (t(sub cr)H(sub 0) approximately less than 0.02) makes it hard to understand why they are observable at all. Our dissipationless N-body simulations show that within a single rich collapsing group compact groups of galaxies continually form. The mean lifetime of a particular compact configuration if approximately 1 Gyr. On this time scale, members may merge and/or other galaxies in the loose group may join the compact configuration. In other words, compact configurations are continually replaced by new systems. The frequency of this process explains the observability of compact groups. Our model produces compact configurations (compact groups (CG's) with optical properties remarkably similar to Hickson's (1982) compact groups (HCG's): (1) CG's have a frequency distribution of members similar to that of HCG's; (2) CG's are approximately equals 10 times as dense as loose groups; (3) CG's have dynamical properties remarkably similar to those of HCG's; (4) most of the galaxy members of CG's are not merger remnants. The crucial aspect of the model is the relationship between CG's and the surrounding rich loose group. Our model predicts the frequency of occurrence of CG's. A preliminary analysis of 18 rich loose groups is consistent with the model prediction. We suggest further observational tests of the model.
Lubin-Tate extensions, an elementary approach

NASA Astrophysics Data System (ADS)

Ershov, Yu L.

2007-12-01

We give an elementary proof of the assertion that the Lubin-Tate extension L\\ge K is an Abelian extension whose Galois group is isomorphic to U_K/N_{L/K}(U_L) for arbitrary fields K that have Henselian discrete valuation rings with finite residue fields. The term `elementary' only means that the proofs are algebraic (that is, no transcedental methods are used [1], pp. 327, 332).
Tool for physics beyond the standard model

NASA Astrophysics Data System (ADS)

Newby, Christopher A.

The standard model (SM) of particle physics is a well studied theory, but there are hints that the SM is not the final story. What the full picture is, no one knows, but this thesis looks into three methods useful for exploring a few of the possibilities. To begin I present a paper by Spencer Chang, Nirmal Raj, Chaowaroj Wanotayaroj, and me, that studies the Higgs boson. The scalar particle first seen in 2012 may be the vanilla SM version, but there is some evidence that its couplings are different than predicted. By means of increasing the Higgs' coupling to vector bosons and fermions, we can be more consistent with the data. Next, in a paper by Spencer Chang, Gabriel Barello, and me, we elaborate on a tool created to study dark matter (DM) direct detection. The original work by Anand. et al. focused on elastic dark matter, whereas we extended this work to include the in elastic case, where different DM mass states enter and leave the collision. We also examine several direct detection experiments with our new framework to see if DAMA's modulation can be explained while avoiding the strong constraints imposed by the other experiments. We find that there are several operators that can do this. Finally, in a paper by Spencer Chang, Gabriel Barello, and me, we study an interesting phenomenon know as kinetic mixing, where two gauge bosons can share interactions with particles even though these particles aren't charged under both gauge groups. This, in and of itself, is not new, but we discuss a different method of obtaining this mixing where instead of mixing between two Abelian groups one of the groups is Nonabelian. Using this we then see that there is an inherent mass scale in the mixing strength; something that is absent in the Abelian-Abelian case. Furthermore, if the Nonabelian symmetry is the SU(2)L of the SM then the mass scale of the physics responsible for the mixing is about 1 TeV, right around the sweet spot for detection at the LHC. This dissertation includes previously published and unpublishedco-authored material.
Where are compact groups in the local Universe?

NASA Astrophysics Data System (ADS)

Díaz-Giménez, Eugenia; Zandivarez, Ariel

2015-06-01

Aims: The purpose of this work is to perform a statistical analysis of the location of compact groups in the Universe from observational and semi-analytical points of view. Methods: We used the velocity-filtered compact group sample extracted from the Two Micron All Sky Survey for our analysis. We also used a new sample of galaxy groups identified in the 2M++ galaxy redshift catalogue as tracers of the large-scale structure. We defined a procedure to search in redshift space for compact groups that can be considered embedded in other overdense systems and applied this criterion to several possible combinations of different compact and galaxy group subsamples. We also performed similar analyses for simulated compact and galaxy groups identified in a 2M++ mock galaxy catalogue constructed from the Millennium Run Simulation I plus a semi-analytical model of galaxy formation. Results: We observed that only ~27% of the compact groups can be considered to be embedded in larger overdense systems, that is, most of the compact groups are more likely to be isolated systems. The embedded compact groups show statistically smaller sizes and brighter surface brightnesses than non-embedded systems. No evidence was found that embedded compact groups are more likely to inhabit galaxy groups with a given virial mass or with a particular dynamical state. We found very similar results when the analysis was performed using mock compact and galaxy groups. Based on the semi-analytical studies, we predict that 70% of the embedded compact groups probably are 3D physically dense systems. Finally, real space information allowed us to reveal the bimodal behaviour of the distribution of 3D minimum distances between compact and galaxy groups. Conclusions: The location of compact groups should be carefully taken into account when comparing properties of galaxies in environments that are a priori different. Appendices are available in electronic form at http://www.aanda.orgFull Tables B.1 and B.2 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/578/A61
Gauge interaction as periodicity modulation

NASA Astrophysics Data System (ADS)

Dolce, Donatello

2012-06-01

The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space-time dimensions (Dolce, 2011) [8]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space-time coordinates. Therefore gauge interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space-time local symmetries. In the approximation of local infinitesimal isometric transformations, Maxwell's kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.
M5-brane and D-brane scattering amplitudes

NASA Astrophysics Data System (ADS)

Heydeman, Matthew; Schwarz, John H.; Wen, Congkao

2017-12-01

We present tree-level n-particle on-shell scattering amplitudes of various brane theories with 16 conserved supercharges. These include the world-volume theory of a probe D3-brane or D5-brane in 10D Minkowski spacetime as well as a probe M5-brane in 11D Minkowski spacetime, which describes self interactions of an abelian tensor supermultiplet with 6D (2, 0) supersymmetry. Twistor-string-like formulas are proposed for tree-level scattering amplitudes of all multiplicities for each of these theories. The R symmetry of the D3-brane theory is shown to be SU(4) × U(1), and the U(1) factor implies that its amplitudes are helicity conserving. Each of 6D theories (D5-brane and M5-brane) reduces to the D3-brane theory by dimensional reduction. As special cases of the general M5-brane amplitudes, we present compact formulas for examples involving only the self-dual B field with n = 4, 6, 8.
The Kitaev honeycomb model on surfaces of genus g ≥ 2

NASA Astrophysics Data System (ADS)

Brennan, John; Vala, Jiří

2018-05-01

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled {Z}}}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Suganuma, Hideo; Sakumichi, Naoyuki

In the context of the dual superconductor picture for the confinement mechanism, we study maximally Abelian (MA) projection of quark confinement in SU(3) quenched lattice QCD with 32{sup 4} at β=6.4 (i.e., a ≃ 0.058 fm). We investigate the static quark-antiquark potential V(r), its Abelian part V{sub Abel}(r) and its off-diagonal part V{sub off}(r), respectively, from the on-axis lattice data. As a remarkable fact, we find almost perfect Abelian dominance for quark confinement, i.e., σ{sub Abel} ≃ σ for the string tension, on the fine and large-volume lattice. We find also a nontrivial summation relation of V (r) ≃ V{submore » Abel}(r)+V{sub off}(r)« less
Non-Abelian gauge fields

NASA Astrophysics Data System (ADS)

Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus

2013-07-01

Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another interesting and related effect, which arises from the interplay between strong magnetic field and lattice potentials, is the famous Hofstadter butterfly: the energy spectrum of a single particle moving on a lattice and subjected to a strong magnetic field displays a beautiful fractal structure as a function of the magnetic flux penetrating each elementary plaquette of the lattice. When the effects of interparticle interactions become dominant, two-dimensional gases of electrons exhibit even more exotic behaviour leading to the fractional quantum Hall effect. In certain conditions such a strongly interacting electron gas may form a highly correlated state of matter, the prototypical example being the celebrated Laughlin quantum liquid. Even more fascinating is the behaviour of bulk excitations (quasi-hole and quasi-particles): they are neither fermionic nor bosonic, but rather behave as anyons with fractional statistics intermediate between the two. Moreover, for some specific filling factors (ratio between the electronic density and the flux density), these anyons are proven to have an internal structure (several components) and non-Abelian braiding properties. Many of the above statements concern theoretical predictions—they have never been observed in condensed matter systems. For instance, the fractional values of the Hall conductance is seen as a direct consequence of the fractional statistics, but to date direct observation of anyons has not been possible in two-dimensional semiconductors. Realizing these predictions in experiments with atoms, ions, photons etc, which potentially allow the experimentalist to perform measurements complementary to those made in condensed matter systems, is thus highly desirable! Non-Abelian gauge fields couple the motional states of the particles to their internal degrees of freedom (such as hyperfine states for atoms or ions, electronic spins for electrons, etc). In this sense external non-Abelian fields extend the concept of spin-orbit coupling (Rashba and Dresselhaus couplings), familiar from AMO and condensed matter physics. They lead to yet another variety of fascinating phenomena such as the quantum spin Hall effect, three-dimensional topological insulators, topological superconductors and superfluids of various kinds. One also expects here the appearance of excitations in a form of topological edge states that can support robust transport, or entangled Majorana fermions in the case of topological superconductors or superfluids. Again, while many kinds of topological insulators have been realized in condensed matter systems, a controlled way of creating them in AMO systems and studying quantum phase transitions between various kinds of them is obviously very appealing and challenging. The various systems listed so far correspond to static gauge fields, which are externally imposed by the experimentalists. Even more fascinating is the possibility of generating synthetically dynamical gauge fields, i.e. gauge fields that evolve in time according to an interacting gauge theory, e.g., a full lattice gauge theory (LGT). These dynamical gauge fields can also couple to matter fields, allowing the quantum simulation of such complex systems (notoriously hard to simulate using 'traditional' computers), which are particularly relevant for modern high-energy physics. So far, most of the theoretical proposals concern the simulation of Abelian gauge theories, however, several groups have recently proposed extensions to the non-Abelian scenarios. The scope of the present focused issue of Journal of Physics B is to cover all of these developments, with particular emphasis on the non-Abelian gauge fields. The 14 papers in this issue include contributions from the leading theory groups working in this field; we believe that this collection will provide the reference set for quantum simulations of gauge fields. Although the special issue contains exclusively theoretical proposals and studies, it should be stressed that the progress in experimental studies of artificial Abelian and non-Abelian gauge fields in recent years has been simply spectacular. Multiple leading groups are working on this subject and have already obtained a lot of seminal results. The papers in the special issue are ordered according to the date of acceptance. The issue opens with a review article by Zhou et al [1] on unconventional states of bosons with synthetic spin-orbit coupling. Next, the paper by Maldonado-Mundo et al [2] studies ultracold Fermi gases with artificial Rashba spin-orbit coupling in a 2D gas. Anderson and Charles [3], in contrast, discuss a three-dimensional spin-orbit coupling in a trap. Orth et al [4] investigate correlated topological phases and exotic magnetism with ultracold fermions, again in the presence of artificial gauge fields. The paper of Nascimbène [5] does not address the synthetic gauge fields directly, but describes an experimental proposal for realizing one-dimensional topological superfluids with ultracold atomic gases; obviously, this problem is well situated in the general and growing field of topological superfluids, in particular those realized in the presence of non-Abelian gauge fields/spin-orbit coupling. Graß et al [6] consider in their paper fractional quantum Hall states of a Bose gas with spin-orbit coupling induced by a laser. Particular attention is drawn here to the possibility of realizing states with non-Abelian anyonic excitations. Zheng et al [7] study properties of Bose gases with Raman-induced spin-orbit coupling. Kiffner et al [8] in their paper touch on another kind of system, namely ultracold Rydberg atoms. In particular they study the generation of Abelian and non-Abelian gauge fields in dipole-dipole interacting Rydberg atoms. The behaviour of fermions in synthetic non-Abelian gauge potentials is discussed by Shenoy and Vyasanakere [9]. The paper starts with the study of Rashbon condensates (i.e. Bose condensates in the presence of Rashba coupling) and also introduces novel kinds of exotic Hamiltonians. Goldman et al [10] propose a concrete setup for realizing arbitrary non-Abelian gauge potentials in optical square lattices; they discuss how such synthetic gauge fields can be exploited to generate Chern insulators. Zygelman [11], similarly as Kiffner et al [8], discusses in his paper non-Abelian gauge fields in Rydberg systems. Marchukov et al [12] return to the subject of spin-orbit coupling, and investigate spectral gaps of spin-orbit coupled particles in the realistic situations of deformed traps. The last two papers, in contrast, are devoted to different subjects. Edmonds et al [13] consider a 'dynamical' density-dependent gauge potential, and study the Josephson effect in a Bose-Einstein condensate subject to such a potential. Last, but not least, Mazzucchi et al [14] study the properties of semimetal-superfluid quantum phase transitions in 3D lattices with Dirac points. References [1] Zhou X, Li Y, Cai Z and Wu C 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134001 [2] Maldonado-Mundo D, Öhberg P and Valiente M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134002 [3] Anderson B M and Clark C W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134003 [4] Orth P P, Cocks D, Rachel S, Buchhold M, Le Hur K and Hofstetter W 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134004 [5] Nascimbène S 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134005 [6] Graß T, Juliá-Díaz B, Burrello M and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134006 [7] Zheng W, Yu Z-Q, Cui X and Zhai H 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134007 [8] Kiffner M, Li W and Jaksch D 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134008 [9] Shenoy V B and Vyasanakere J P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134009 [10] Goldman N, Gerbier F and Lewenstein M 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134010 [11] Zygelman B 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134011 [12] Marchukov O V, Volosniev A G, Fedorov D V, Jensen A S and Zinner N T 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134012 [13] Edmonds M J, Valiente M and Öhberg P 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134013 [14] Mazzucchi G, Lepori L and Trombettoni A 2013 J. Phys. B: At. Mol. Opt. Phys. 46 134014
Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE PAGES

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; ...

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less
Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme-tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one andmore » two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro-modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. Lastly, we describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.« less
Light chiral dark sector

NASA Astrophysics Data System (ADS)

Harigaya, Keisuke; Nomura, Yasunori

2016-08-01

An interesting possibility for dark matter is a scalar particle of mass of order 10 MeV-1 GeV, interacting with a U (1 ) gauge boson (dark photon) which mixes with the photon. We present a simple and natural model realizing this possibility. The dark matter arises as a composite pseudo-Nambu-Goldstone boson (dark pion) in a non-Abelian gauge sector, which also gives a mass to the dark photon. For a fixed non-Abelian gauge group, S U (N ) , and a U (1 ) charge of the constituent dark quarks, the model has only three free parameters: the dynamical scale of the non-Abelian gauge theory, the gauge coupling of the dark photon, and the mixing parameter between the dark and standard model photons. In particular, the gauge symmetry of the model does not allow any mass term for the dark quarks, and the stability of the dark pion is understood as a result of an accidental global symmetry. The model has a significant parameter space in which thermal relic dark pions comprise all of the dark matter, consistently with all experimental and cosmological constraints. In a corner of the parameter space, the discrepancy of the muon g -2 between experiments and the standard model prediction can also be ameliorated due to a loop contribution of the dark photon. Smoking-gun signatures of the model include a monophoton signal from the e+e- collision into a photon and a "dark rho meson." Observation of two processes in e+e- collision—the mode into the dark photon and that into the dark rho meson—would provide strong evidence for the model.
Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods

NASA Astrophysics Data System (ADS)

James, Andrew J. A.; Konik, Robert M.; Lecheminant, Philippe; Robinson, Neil J.; Tsvelik, Alexei M.

2018-04-01

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb–Liniger model, 1 + 1D quantum chromodynamics, as well as Landau–Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-Abelian bosonization to truncated spectrum methods.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil J; Tsvelik, Alexei M

2018-02-26

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1 + 1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.
Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.
Imaging Anyons with Scanning Tunneling Microscopy

NASA Astrophysics Data System (ADS)

Papić, Zlatko; Mong, Roger S. K.; Yazdani, Ali; Zaletel, Michael P.

2018-01-01

Anyons are exotic quasiparticles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-Abelian statistics—a property that would help realize fault-tolerant quantum computation. Non-Abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases in the presence of a large magnetic field, such as the ν =5 /2 FQH state. However, direct experimental evidence of anyons and tests that can distinguish between Abelian and non-Abelian quantum ground states with such excitations have remained elusive. Here, we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the STM. Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect—and perhaps ultimately manipulate—these exotic quasiparticles.

Dephasing in a 5/2 quantum Hall Mach-Zehnder interferometer due to the presence of neutral edge modes

NASA Astrophysics Data System (ADS)

Dinaii, Yehuda; Goldstein, Moshe; Gefen, Yuval

Non-Abelian statistics is an intriguing feature predicted to characterize quasiparticles in certain topological phases of matter. This property is both fascinating on the theoretical side and the key ingredient for the implementation of future topological quantum computers. A smoking gun manifestation of non-Abelian statistics consists of demonstrating that braiding of quasiparticles leads to transitions among different states in the relevant degenerate Hilbert manifold. This can be achieved utilizing a Mach-Zehnder interferometer, where Coulomb effects can be neglected, and the electric current is expected to carry clear signatures of non-Abelianity. Here we argue that attempts to measure non-Abelian statistics in the prominent quantum Hall fraction of 5/2 may fail; this can be understood by studying the corresponding edge theory at finite temperatures and bias. We find that the presence of neutral modes imposes stronger limitations on the experimental conditions as compared to quantum Hall states that do not support neutral edge modes. We discuss how to overcome this hindrance. Interestingly, neutral-mode-induced dephasing can be quite different in the Pfaffian state as compared to the anti-Pfaffian state, if the neutral and charge velocities are comparable.
Nilpotent symmetries and Curci-Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

NASA Astrophysics Data System (ADS)

Srinivas, N.; Malik, R. P.

2017-11-01

We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.
Wilson-loop instantons

NASA Technical Reports Server (NTRS)

Lee, Kimyeong; Holman, Richard; Kolb, Edward W.

1987-01-01

Wilson-loop symmetry breaking is considered on a space-time of the form M4 x K, where M4 is a four-dimensional space-time and K is an internal space with nontrivial and finite fundamental group. It is shown in a simple model that the different vacua obtained by breaking a non-Abelian gauge group by Wilson loops are separated in the space of gauge potentials by a finite energy barrier. An interpolating gauge configuration is then constructed between these vacua and shown to have minimum energy. Finally some implications of this construction are discussed.
Constructive tensorial group field theory II: the {U(1)-T^4_4} model

NASA Astrophysics Data System (ADS)

Lahoche, Vincent

2018-05-01

In this paper, we continue our program of non-pertubative constructions of tensorial group field theories (TGFT). We prove analyticity and Borel summability in a suitable domain of the coupling constant of the simplest super-renormalizable TGFT which contains some ultraviolet divergencies, namely the color-symmetric quartic melonic rank-four model with Abelian gauge invariance, nicknamed . We use a multiscale loop vertex expansion. It is an extension of the loop vertex expansion (the basic constructive technique for non-local theories) which is required for theories that involve non-trivial renormalization.
Supertranslations and Superrotations at the Black Hole Horizon.

PubMed

Donnay, Laura; Giribet, Gaston; González, Hernán A; Pino, Miguel

2016-03-04

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.
Gerbes, M5-Brane Anomalies and E8 Gauge Theory

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Jurco, Branislav

2004-10-01

Abelian gerbes and twisted bundles describe the topology of the NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general tilde OmegaE8, the central extension of the E8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form field strength G and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.
Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

DOE PAGES

Cvetič, Mirjam; Grassi, Antonella; Poretschkin, Maximilian

2017-06-30

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairsmore » for symmetric examples with Z 2 and Z 3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.« less
Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cvetič, Mirjam; Grassi, Antonella; Poretschkin, Maximilian

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairsmore » for symmetric examples with Z 2 and Z 3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.« less
Holonomy of a principal composite bundle connection, non-Abelian geometric phases, and gauge theory of gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Viennot, David

We show that the holonomy of a connection defined on a principal composite bundle is related by a non-Abelian Stokes theorem to the composition of the holonomies associated with the connections of the component bundles of the composite. We apply this formalism to describe the non-Abelian geometric phase (when the geometric phase generator does not commute with the dynamical phase generator). We find then an assumption to obtain a new kind of separation between the dynamical and the geometric phases. We also apply this formalism to the gauge theory of gravity in the presence of a Dirac spinor field inmore » order to decompose the holonomy of the Lorentz connection into holonomies of the linear connection and of the Cartan connection.« less
Route to non-Abelian quantum turbulence in spinor Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Mawson, Thomas; Ruben, Gary; Simula, Tapio

2015-06-01

We have studied computationally the collision dynamics of spin-2 Bose-Einstein condensates initially confined in a triple-well trap. Depending on the phase structure of the initial-state spinor wave function, the collision of the three condensate fragments produces one of many possible vortex-antivortex lattices, after which the system transitions to quantum turbulence. We find that the emerging vortex lattice structures can be described in terms of multiwave interference. We show that the three-fragment collisions can be used to systematically produce staggered vortex-antivortex honeycomb lattices of fractional-charge vortices, whose collision dynamics are known to be non-Abelian. Such condensate collider experiments could potentially be used as a controllable pathway to generating non-Abelian superfluid turbulence with networks of vortex rungs.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.

PubMed

Brihaye, Yves; Radu, Eugen; Tchrakian, D H

2011-02-18

We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.
Construction of non-Abelian gauge theories on noncommutative spaces

NASA Astrophysics Data System (ADS)

Jurčo, B.; Möller, L.; Schraml, S.; Schupp, P.; Wess, J.

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.
LETTER TO THE EDITOR: Bicomplexes and conservation laws in non-Abelian Toda models

NASA Astrophysics Data System (ADS)

Gueuvoghlanian, E. P.

2001-08-01

A bicomplex structure is associated with the Leznov-Saveliev equation of integrable models. The linear problem associated with the zero-curvature condition is derived in terms of the bicomplex linear equation. The explicit example of a non-Abelian conformal affine Toda model is discussed in detail and its conservation laws are derived from the zero-curvature representation of its equation of motion.
The Optical Green Valley Versus Mid-infrared Canyon in Compact Groups

NASA Technical Reports Server (NTRS)

Walker, Lisa May; Butterfield, Natalie; Johnson, Kelsey; Zucker, Catherine; Gallagher, Sarah; Konstantopoulos, Iraklis; Zabludoff, Ann; Hornschemeier, Ann E.; Tzanavaris, Panayiotis; Charlton, Jane C.

2013-01-01

Compact groups of galaxies provide conditions similar to those experienced by galaxies in the earlier universe. Recent work on compact groups has led to the discovery of a dearth of mid-infrared transition galaxies (MIRTGs) in Infrared Array Camera (3.6-8.0 micrometers) color space as well as at intermediate specific star formation rates. However, we find that in compact groups these MIRTGs have already transitioned to the optical ([g-r]) red sequence. We investigate the optical color-magnitude diagram (CMD) of 99 compact groups containing 348 galaxies and compare the optical CMD with mid-infrared (mid-IR) color space for compact group galaxies. Utilizing redshifts available from Sloan Digital Sky Survey, we identified new galaxy members for four groups. By combining optical and mid-IR data, we obtain information on both the dust and the stellar populations in compact group galaxies. We also compare with more isolated galaxies and galaxies in the Coma Cluster, which reveals that, similar to clusters, compact groups are dominated by optically red galaxies. While we find that compact group transition galaxies lie on the optical red sequence, LVL (Local Volume Legacy) + (plus) SINGS (Spitzer Infrared Nearby Galaxies Survey) mid-IR (infrared) transition galaxies span the range of optical colors. The dearth of mid-IR transition galaxies in compact groups may be due to a lack of moderately star-forming low mass galaxies; the relative lack of these galaxies could be due to their relatively small gravitational potential wells. This makes them more susceptible to this dynamic environment, thus causing them to more easily lose gas or be accreted by larger members.
Upper bound on the Abelian gauge coupling from asymptotic safety

NASA Astrophysics Data System (ADS)

Eichhorn, Astrid; Versteegen, Fleur

2018-01-01

We explore the impact of asymptotically safe quantum gravity on the Abelian gauge coupling in a model including a charged scalar, confirming indications that asymptotically safe quantum fluctuations of gravity could trigger a power-law running towards a free fixed point for the gauge coupling above the Planck scale. Simultaneously, quantum gravity fluctuations balance against matter fluctuations to generate an interacting fixed point, which acts as a boundary of the basin of attraction of the free fixed point. This enforces an upper bound on the infrared value of the Abelian gauge coupling. In the regime of gravity couplings which in our approximation also allows for a prediction of the top quark and Higgs mass close to the experimental value [1], we obtain an upper bound approximately 35% above the infrared value of the hypercharge coupling in the Standard Model.
Inhomogeneous Einstein-Rosen string cosmology

NASA Astrophysics Data System (ADS)

Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza

1999-08-01

Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VIh cosmology. The asymptotic behavior of the solutions is investigated and further applications are briefly discussed.
Cheshire charge in (3+1)-dimensional topological phases

NASA Astrophysics Data System (ADS)

Else, Dominic V.; Nayak, Chetan

2017-07-01

We show that (3 +1 ) -dimensional topological phases of matter generically support loop excitations with topological degeneracy. The loops carry "Cheshire charge": topological charge that is not the integral of a locally defined topological charge density. Cheshire charge has previously been discussed in non-Abelian gauge theories, but we show that it is a generic feature of all (3+1)-D topological phases (even those constructed from an Abelian gauge group). Indeed, Cheshire charge is closely related to nontrivial three-loop braiding. We use a dimensional reduction argument to compute the topological degeneracy of loop excitations in the (3 +1 ) -dimensional topological phases associated with Dijkgraaf-Witten gauge theories. We explicitly construct membrane operators associated with such excitations in soluble microscopic lattice models in Z2×Z2 Dijkgraaf-Witten phases and generalize this construction to arbitrary membrane-net models. We explain why these loop excitations are the objects in the braided fusion 2-category Z (2 VectGω) , thereby supporting the hypothesis that 2-categories are the correct mathematical framework for (3 +1 ) -dimensional topological phases.
Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

opens the door for exciting new research directions, such as quantum simulation of the Schwinger model and of non-Abelian models. (a) Papers...exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian
Existence of topological multi-string solutions in Abelian gauge field theories

NASA Astrophysics Data System (ADS)

Han, Jongmin; Sohn, Juhee

2017-11-01

In this paper, we consider a general form of self-dual equations arising from Abelian gauge field theories coupled with the Einstein equations. By applying the super/subsolution method, we prove that topological multi-string solutions exist for any coupling constant, which improves previously known results. We provide two examples for application: the self-dual Einstein-Maxwell-Higgs model and the gravitational Maxwell gauged O(3) sigma model.
Light chiral dark sector

DOE PAGES

Harigaya, Keisuke; Nomura, Yasunori

2016-08-11

An interesting possibility for dark matter is a scalar particle of mass of order 10 MeV-1 GeV, interacting with a U(1) gauge boson (dark photon) which mixes with the photon. We present a simple and natural model realizing this possibility. The dark matter arises as a composite pseudo-Nambu-Goldstone boson (dark pion) in a non-Abelian gauge sector, which also gives a mass to the dark photon. For a fixed non-Abelian gauge group, SU(N), and a U(1) charge of the constituent dark quarks, the model has only three free parameters: the dynamical scale of the non-Abelian gauge theory, the gauge coupling ofmore » the dark photon, and the mixing parameter between the dark and standard model photons. In particular, the gauge symmetry of the model does not allow any mass term for the dark quarks, and the stability of the dark pion is understood as a result of an accidental global symmetry. The model has a significant parameter space in which thermal relic dark pions comprise all of the dark matter, consistently with all experimental and cosmological constraints. In a corner of the parameter space, the discrepancy of the muon g-2 between experiments and the standard model prediction can also be ameliorated due to a loop contribution of the dark photon. Smoking-gun signatures of the model include a monophoton signal from the e +e - collision into a photon and a "dark rho meson." Observation of two processes in e +e - collision - the mode into the dark photon and that into the dark rho meson - would provide strong evidence for the model.« less

Light chiral dark sector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harigaya, Keisuke; Nomura, Yasunori

An interesting possibility for dark matter is a scalar particle of mass of order 10 MeV-1 GeV, interacting with a U(1) gauge boson (dark photon) which mixes with the photon. We present a simple and natural model realizing this possibility. The dark matter arises as a composite pseudo-Nambu-Goldstone boson (dark pion) in a non-Abelian gauge sector, which also gives a mass to the dark photon. For a fixed non-Abelian gauge group, SU(N), and a U(1) charge of the constituent dark quarks, the model has only three free parameters: the dynamical scale of the non-Abelian gauge theory, the gauge coupling ofmore » the dark photon, and the mixing parameter between the dark and standard model photons. In particular, the gauge symmetry of the model does not allow any mass term for the dark quarks, and the stability of the dark pion is understood as a result of an accidental global symmetry. The model has a significant parameter space in which thermal relic dark pions comprise all of the dark matter, consistently with all experimental and cosmological constraints. In a corner of the parameter space, the discrepancy of the muon g-2 between experiments and the standard model prediction can also be ameliorated due to a loop contribution of the dark photon. Smoking-gun signatures of the model include a monophoton signal from the e +e - collision into a photon and a "dark rho meson." Observation of two processes in e +e - collision - the mode into the dark photon and that into the dark rho meson - would provide strong evidence for the model.« less
Functional renormalization group for the U (1 )-T56 tensorial group field theory with closure constraint

NASA Astrophysics Data System (ADS)

Lahoche, Vincent; Ousmane Samary, Dine

2017-02-01

This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.
Quantum Chromodynamics and Color Confinement (confinement 2000) - Proceedings of the International Symposium

NASA Astrophysics Data System (ADS)

Suganuma, H.; Fukushima, M.; Toki, H.

The Table of Contents for the book is as follows: * Preface * Opening Address * Monopole Condensation and Quark Confinement * Dual QCD, Effective String Theory, and Regge Trajectories * Abelian Dominance and Monopole Condensation * Non-Abelian Stokes Theorem and Quark Confinement in QCD * Infrared Region of QCD and Confining Configurations * BRS Quartet Mechanism for Color Confinement * Color Confinement and Quartet Mechanism * Numerical Tests of the Kugo-Ojima Color Confinement Criterion * Monopoles and Confinement in Lattice QCD * SU(2) Lattice Gauge Theory at T > 0 in a Finite Box with Fixed Holonomy * Confining and Dirac Strings in Gluodynamics * Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory * Quark Confinement Physics from Lattice QCD * An (Almost) Perfect Lattice Action for SU(2) and SU(3) Gluodynamics * Vortices and Confinement in Lattice QCD * P-Vortices, Nexuses and Effects of Gribov Copies in the Center Gauges * Laplacian Center Vortices * Center Vortices at Strong Couplings and All Couplings * Simulations in SO(3) × Z(2) Lattice Gauge Theory * Exciting a Vortex - the Cost of Confinement * Instantons in QCD * Deformation of Instanton in External Color Fields * Field Strength Correlators in the Instanton Liquid * Instanton and Meron Physics in Lattice QCD * The Dual Ginzburg-Landau Theory for Confinement and the Role of Instantons * Lattice QCD for Quarks, Gluons and Hadrons * Hadronic Spectral Functions in QCD * Universality and Chaos in Quantum Field Theories * Lattice QCD Study of Three Quark Potential * Probing the QCD Vacuum with Flavour Singlet Objects : η' on the Lattice * Lattice Studies of Quarks and Gluons * Quarks and Hadrons in QCD * Supersymmetric Nonlinear Sigma Models * Chiral Transition and Baryon-number Susceptibility * Light Quark Masses in QCD * Chiral Symmetry of Baryons and Baryon Resonances * Confinement and Bound States in QCD * Parallel Session * Off-diagonal Gluon Mass Generation and Strong Randomness of Off-diagonal Gluon Phase in the Maximally Abelian Gauge * On the Colour Confinement and the Minimal Surface * Glueball Mass and String Tension of SU(2) Gluodynamics from Abelian Monopoles and Strings * Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio Model at Finite Temperature and Density * Confining Flux-Tube and Hadrons in QCD * Gauge Symmetry Breakdown due to Dynamical Higgs Scalar * Spatial Structure of Quark Cooper Pairs * New Approach to Axial Coupling Constants in the QCD Sum Rule and Instanton Effects * String Breaking on a Lattice * Bethe-Salpeter Approach for Mesons within the Dual Ginzburg-Landau Theory * Gauge Dependence and Matching Procedure of a Nonrelativistic QCD Boundstate Formalism * A Mathematical Approach to the SU(2)-Quark Confinement * Simulations of Odd Flavors QCD by Hybrid Monte Carlo * Non-Perturbative Renormalization Group Analysis of Dynamical Chiral Symmetry Breaking with Beyond Ladder Contributions * Charmonium Physics in Finite Temperature Lattice QCD * From Meson-Nucleon Scattering to Vector Mesons in Nuclear Matter * Symposium Program * List of Participants
A new construction of rational electromagnetic knots

NASA Astrophysics Data System (ADS)

Lechtenfeld, Olaf; Zhilin, Gleb

2018-06-01

We set up a correspondence between solutions of the Yang-Mills equations on R ×S3 and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we present a straightforward algorithm to generate an infinite number of explicit solutions, with fields and potentials in Minkowski coordinates given by rational functions of increasing complexity. We illustrate our method with a nontrivial example.
Disassembling the clockwork mechanism

NASA Astrophysics Data System (ADS)

Craig, Nathaniel; Garcia Garcia, Isabel; Sutherland, Dave

2017-10-01

The clockwork mechanism is a means of naturally generating exponential hierarchies in theories without significant hierarchies among fundamental parameters. We emphasize the role of interactions in the clockwork mechanism, demonstrating that clockwork is an intrinsically abelian phenomenon precluded in non-abelian theories such as Yang-Mills, non-linear sigma models, and gravity. We also show that clockwork is not realized in extra-dimensional theories through purely geometric effects, but may be generated by appropriate localization of zero modes.
Flavored gauge mediation with discrete non-Abelian symmetries

NASA Astrophysics Data System (ADS)

Everett, Lisa L.; Garon, Todd S.

2018-05-01

We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the S U (2 ) messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S3 Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe μ /Bμ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that μ and Bμ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetry-breaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.
Magnetic monopole versus vortex as gauge-invariant topological objects for quark confinement

NASA Astrophysics Data System (ADS)

Kondo, Kei-Ichi; Sasago, Takaaki; Shinohara, Toru; Shibata, Akihiro; Kato, Seikou

2017-12-01

First, we give a gauge-independent definition of chromomagnetic monopoles in SU(N) Yang-Mills theory which is derived through a non-Abelian Stokes theorem for the Wilson loop operator. Then we discuss how such magnetic monopoles can give a nontrivial contribution to the Wilson loop operator for understanding the area law of the Wilson loop average. Next, we discuss how the magnetic monopole condensation picture are compatible with the vortex condensation picture as another promising scenario for quark confinement. We analyze the profile function of the magnetic flux tube as the non-Abelian vortex solution of U(N) gauge-Higgs model, which is to be compared with numerical simulations of the SU(N) Yang-Mills theory on a lattice. This analysis gives an estimate of the string tension based on the vortex condensation picture, and possible interactions between two non-Abelian vortices.
Diffusion of massive particles around an Abelian-Higgs string

NASA Astrophysics Data System (ADS)

Saha, Abhisek; Sanyal, Soma

2018-03-01

We study the diffusion of massive particles in the space time of an Abelian Higgs string. The particles in the early universe plasma execute Brownian motion. This motion of the particles is modeled as a two dimensional random walk in the plane of the Abelian Higgs string. The particles move randomly in the space time of the string according to their geodesic equations. We observe that for certain values of their energy and angular momentum, an overdensity of particles is observed close to the string. We find that the string parameters determine the distribution of the particles. We make an estimate of the density fluctuation generated around the string as a function of the deficit angle. Though the thickness of the string is small, the length is large and the overdensity close to the string may have cosmological consequences in the early universe.
Symmetry enhancement of extremal horizons in D = 5 supergravity

NASA Astrophysics Data System (ADS)

Kayani, U.

2018-06-01

We consider the near-horizon geometry of supersymmetric extremal black holes in un-gauged and gauged 5-dimensional supergravity, coupled to abelian vector multiplets. By analyzing the global properties of the Killing spinors, we prove that the near-horizon geometries undergo a supersymmetry enhancement. This follows from a set of generalized Lichnerowicz-type theorems we establish, together with an index theory argument. As a consequence, these solutions always admit a symmetry group.
Asymptotically safe standard model extensions?

NASA Astrophysics Data System (ADS)

Pelaggi, Giulio Maria; Plascencia, Alexis D.; Salvio, Alberto; Sannino, Francesco; Smirnov, Juri; Strumia, Alessandro

2018-05-01

We consider theories with a large number NF of charged fermions and compute the renormalization group equations for the gauge, Yukawa and quartic couplings resummed at leading order in 1 /NF. We construct extensions of the standard model where SU(2) and/or SU(3) are asymptotically safe. When the same procedure is applied to the Abelian U(1) factor, we find that the Higgs quartic can not be made asymptotically safe and stay perturbative at the same time.
Stealth configurations in vector-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Chagoya, Javier; Tasinato, Gianmassimo

2018-01-01

Studying the physics of compact objects in modified theories of gravity is important for understanding how future observations can test alternatives to General Relativity. We consider a subset of vector-tensor Galileon theories of gravity characterized by new symmetries, which can prevent the propagation of the vector longitudinal polarization, even in absence of Abelian gauge invariance. We investigate new spherically symmetric and slowly rotating solutions for these systems, including an arbitrary matter Lagrangian. We show that, under certain conditions, there always exist stealth configurations whose geometry coincides with solutions of Einstein gravity coupled with the additional matter. Such solutions have a non-trivial profile for the vector field, characterized by independent integration constants, which extends to asymptotic infinity. We interpret our findings in terms of the symmetries and features of the original vector-tensor action, and on the number of degrees of freedom that it propagates. These results are important to eventually describe gravitationally bound configurations in modified theories of gravity, such as black holes and neutron stars, including realistic matter fields forming or surrounding the object.
Gauge equivalence of two different IAnsaaumlItze Rfor non-Abelian charged vortices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paul, S.K.

1987-05-15

Recently the existence of non-Abelian charged vortices has been established by taking two different Ansa$uml: tze in SU(2) gauge theories. We point out that these two Ansa$uml: tze are in two topologically equivalent prescriptions. We show that they are gauge equivalent only at infinity. We also show that this gauge equivalence is not possible for Z/sub N/ vortices in SU(N) gauge theories for Ngreater than or equal to3.
Stability of infinite derivative Abelian Higgs models

NASA Astrophysics Data System (ADS)

Ghoshal, Anish; Mazumdar, Anupam; Okada, Nobuchika; Villalba, Desmond

2018-04-01

Motivated by the stringy effects by modifying the local kinetic term of an Abelian Higgs field by the Gaussian kinetic term, we show that the Higgs field does not possess any instability; the Yukawa coupling between the scalar and the fermion, the gauge coupling, and the self interaction of the Higgs yields exponentially suppressed running at high energies, showing that such class of theory never suffers from vacuum instability. We briefly discuss its implications for the early Universe cosmology.
Continuous Abelian Sandpile Model in Two Dimensional Lattice

NASA Astrophysics Data System (ADS)

Azimi-Tafreshi, N.; Lotfi, E.; Moghimi-Araghi, S.

We investigate a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so the general properties of the two models are identical. Yet the new model allows us to investigate some problems such as the effect of very small mass on the height probabilities, different boundary conditions, etc.
Universal attractor in a highly occupied non-Abelian plasma

NASA Astrophysics Data System (ADS)

Berges, J.; Boguslavski, K.; Schlichting, S.; Venugopalan, R.

2014-06-01

We study the thermalization process in highly occupied non-Abelian plasmas at weak coupling. The nonequilibrium dynamics of such systems is classical in nature and can be simulated with real-time lattice gauge theory techniques. We provide a detailed discussion of this framework and elaborate on the results reported in J. Berges, K. Boguslavski, S. Schlichting, and R. Venugopalan, Phys. Rev. D 89, 074011 (2014), 10.1103/PhysRevD.89.074011 along with novel findings. We demonstrate the emergence of universal attractor solutions, which govern the nonequilibrium evolution on large time scales both for nonexpanding and expanding non-Abelian plasmas. The turbulent attractor for a nonexpanding plasma drives the system close to thermal equilibrium on a time scale t ˜Q-1αs-7/4. The attractor solution for an expanding non-Abelian plasma leads to a strongly interacting albeit highly anisotropic system at the transition to the low-occupancy or quantum regime. This evolution in the classical regime is, within the uncertainties of our simulations, consistent with the "bottom up" thermalization scenario [R. Baier, A. H. Mueller, D. Schiff, and D. T. Son, Phys. Lett. B 502, 51 (2001), 10.1016/S0370-2693(01)00191-5]. While the focus of this paper is to understand the nonequilibrium dynamics in weak coupling asymptotics, we also discuss the relevance of our results for larger couplings in the early time dynamics of heavy ion collision experiments.
Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

NASA Astrophysics Data System (ADS)

Cheng, Meng; Tantivasadakarn, Nathanan; Wang, Chenjie

2018-01-01

We study Abelian braiding statistics of loop excitations in three-dimensional gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic symmetry-protected topological (FSPT) phases with unitary symmetries. It is known that the two problems are related by turning FSPT phases into gauge theories through gauging the global symmetry of the former. We show that there exist certain types of Abelian loop braiding statistics that are allowed only in the presence of fermionic particles, which correspond to 3D "intrinsic" FSPT phases, i.e., those that do not stem from bosonic SPT phases. While such intrinsic FSPT phases are ubiquitous in 2D systems and in 3D systems with antiunitary symmetries, their existence in 3D systems with unitary symmetries was not confirmed previously due to the fact that strong interaction is necessary to realize them. We show that the simplest unitary symmetry to support 3D intrinsic FSPT phases is Z2×Z4. To establish the results, we first derive a complete set of physical constraints on Abelian loop braiding statistics. Solving the constraints, we obtain all possible Abelian loop braiding statistics in 3D gauge theories, including those that correspond to intrinsic FSPT phases. Then, we construct exactly soluble state-sum models to realize the loop braiding statistics. These state-sum models generalize the well-known Crane-Yetter and Dijkgraaf-Witten models.
Entanglement from topology in Chern-Simons theory

NASA Astrophysics Data System (ADS)

Salton, Grant; Swingle, Brian; Walter, Michael

2017-05-01

The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary three-manifolds with a fixed number of torus boundaries in both Abelian U (1 ) and non-Abelian S O (3 ) Chern-Simons theory. For the Abelian theory, we find that the states that can be prepared coincide precisely with the set of stabilizer states from quantum information theory. This constrains the multipartite entanglement present in this theory, but it also reveals that stabilizer states can be described by topology. In particular, we find an explicit expression for the entanglement entropy of a many-torus subsystem using only a single replica, as well as a concrete formula for the number of GHZ states that can be distilled from a tripartite state prepared through path integration. For the non-Abelian theory, we find a notion of "state universality," namely that any state can be prepared to an arbitrarily good approximation. The manifolds we consider can also be viewed as toy models of multiboundary wormholes in AdS/CFT.
Pure gauge spin-orbit couplings

NASA Astrophysics Data System (ADS)

Shikakhwa, M. S.

2017-01-01

Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge field theory. A special class of these fields that, though a 2×2 matrix, are Abelian are seen to emerge and their general form is given. It is shown that the unitary transformation that gauges away these fields induces at the same time a rotation on the wave function about a fixed axis but with a space-dependent angle, both of which being characteristics of the SOI involved. The experimentally important case of equal-strength Rashba and Dresselhaus SOI (R+D SOI) is shown to fall within this special class of Abelian gauge fields, and the phenomenon of persistent spin helix (PSH) that emerges in the presence of this latter SOI in a plane is shown to fit naturally within the general formalism developed. The general formalism is also extended to the case of a particle confined to a ring. It is shown that the Hamiltonian on a ring in the presence of equal-strength R+D SOI is unitarily equivalent to that of a particle subject to only a spin-independent but θ-dependent potential with the unitary transformation relating the two being again the space-dependent rotation operator characteristic of R+D SOI.
Non-Abelian Yang-Mills analogue of classical electromagnetic duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Hong-Mo; Faridani, J.; Tsun, T.S.

The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor {ital T}{sub {mu}{nu}} of the Freedman-Townsend-type. Though not itself functioning as such, {ital T}{sub {mu}{nu}} gives rise to a dual parallel transport {ital {tilde A}}{sub {mu}} for the phase of themore » wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of {ital {tilde A}}{sub {mu}}. At the same time, the gauge symmetry is found doubled from say SU({ital N}) to SU({ital N}){times}SU({ital N}). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ``universal`` principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov.« less
Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions

DOE PAGES

Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; ...

2014-09-25

Here we apply the GLV reaction operator solution to the Vitev-Gunion-Bertsch (VGB) boundary conditions to compute the all-order in nuclear opacity non-abelian gluon bremsstrahlung of event- by-event uctuating beam jets in nuclear collisions. We evaluate analytically azimuthal Fourier moments of single gluon, vmore » $$M\\atop{n}$$ {1}, and even number 2ℓ gluon, v$$M\\atop{n}$$ {2ℓ} inclusive distributions in high energy p+A reactions as a function of harmonic $n$, target recoil cluster number, $M$, and gluon number, 2ℓ, at RHIC and LHC. Multiple resolved clusters of recoiling target beam jets together with the projectile beam jet form Color Scintillation Antenna (CSA) arrays that lead to character- istic boost non-invariant trapezoidal rapidity distributions in asymmetric B+A nuclear collisions. The scaling of intrinsically azimuthally anisotropic and long range in η nature of the non-Abelian bremsstrahlung leads to v n moments that are similar to results from hydrodynamic models, but due entirely to non-Abelian wave interference phenomena sourced by the fluctuating CSA. Our analytic non-flow solutions are similar to recent numerical saturation model predictions but differ by predicting a simple power-law hierarchy of both even and odd v n without invoking k T factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the v n(k Tη). Non- Abelian beam jet bremsstrahlung may thus provide a simple analytic solution to Beam Energy Scan (BES) puzzle of the near $$\\sqrt{s}$$ independence of v n(pT) moments observed down to 10 AGeV where large-x valence quark beam jets dominate inelastic dynamics. Recoil bremsstrahlung from multiple independent CSA clusters could also provide a partial explanation for the unexpected similarity of v n in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.« less
Observational properties of compact groups of galaxies

NASA Technical Reports Server (NTRS)

Hickson, Paul

1990-01-01

Compact groups are small, relatively isolated, systems of galaxies with projected separations comparable to the diameters of the galaxies themselves. Two well-known examples are Stephan's Quintet (Stephan, 1877) and Seyfert's Sextet (Seyfert 1948a,b). In groups such as these, the apparent space density of galaxies approaches 10(exp 6) Mpc(sub -3), denser even than the cores of rich clusters. The apparent unlikeliness of the chance occurrence of such tight groupings lead Ambartsumyan (1958, 1975) to conclude that compact groups must be physically dense systems. This view is supported by clear signs of galaxy interactions that are seen in many groups. Spectroscopic observations reveal that typical relative velocities of galaxies in the groups are comparable to their internal stellar velocities. This should be conducive to strong gravitational interactions - more so than in rich clusters, where galaxy velocities are typically much higher. This suggests that compact groups could be excellent laboratories in which to study galaxy interactions and their effects. Compact groups often contain one or more galaxies whose redshift differs greatly from those of the other group members. If these galaxies are at the same distance as the other members, either entire galaxies are being ejected at high velocities from these groups, or some new physical phenomena must be occurring. If their redshifts are cosmological, we must explain why so many discordant galaxies are found in compact groups. In recent years much progress has been made in addressing these questions. Here, the author discusses the current observational data on compact groups and their implications.
The operator algebra approach to quantum groups

PubMed Central

Kustermans, Johan; Vaes, Stefaan

2000-01-01

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
DOE Office of Scientific and Technical Information (OSTI.GOV)

Osipov, D V

We prove noncommutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws establish that some central extensions of globally constructed groups split over certain subgroups constructed by points or projective curves on a surface. For a two-dimensional local field with a last finite residue field, the local central extension which is constructed is isomorphic to the central extension which comes from the case of tame ramification of the Abelian two-dimensional local Langlands correspondence suggested by Kapranov. Bibliography: 9 titles.
BFV-BRST analysis of equivalence between noncommutative and ordinary gauge theories

NASA Astrophysics Data System (ADS)

Dayi, O. F.

2000-05-01

Constrained hamiltonian structure of noncommutative gauge theory for the gauge group /U(1) is discussed. Constraints are shown to be first class, although, they do not give an Abelian algebra in terms of Poisson brackets. The related BFV-BRST charge gives a vanishing generalized Poisson bracket by itself due to the associativity of /*-product. Equivalence of noncommutative and ordinary gauge theories is formulated in generalized phase space by using BFV-BRST charge and a solution is obtained. Gauge fixing is discussed.
Combinatorial Problems of Applied Discrete Mathematics.

DTIC Science & Technology

1979-12-01

204 .I (30) 3. Steiner, Combinatorische Aufgabe, Z. Reine Angew. Math. 45 (1853) 18 1—182. (31) IC. Takeuchi, A table of difference sets generating...Assoc. Fr. Ay. Sd . 1 (1900) 122— 123; 2 (1901) 170—203. • (33) R.M. Wilson, Cyclotomy and difference fam ilies in elementary Abelian groups , 3. Number...the differe nt cliques containing either A or B. Let us first introduce the following notations. If A is a vertex in G, then 1(A) denotes the set of
Lorentz-violating SO(3) model: Discussing unitarity, causality, and 't Hooft-Polyakov monopoles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scarpelli, A.P. Baeta; Grupo de Fisica Teorica Jose Leite Lopes, Petropolis, RJ; Helayeel-Neto, J.A.

2006-05-15

In this paper, we extend the analysis of the Lorentz-violating Quantum Electrodynamics to the non-Abelian case: an SO(3) Yang-Mills Lagrangian with the addition of the non-Abelian Chern-Simons-type term. We consider the spontaneous symmetry breaking of the model and inspect its spectrum in order to check if unitarity and causality are respected. An analysis of the topological structure is also carried out and we show that a 't Hooft-Polyakov solution for monopoles is still present.
Abelian tensor hierarchy in 4D N = 1 conformal supergravity

NASA Astrophysics Data System (ADS)

Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo

2016-09-01

We consider Abelian tensor hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal tensor calculus.
Various Forms of BRST Symmetry in Abelian 2-FORM Gauge Theory

NASA Astrophysics Data System (ADS)

Rai, Sumit Kumar; Mandal, Bhabani Prasad

We derive the various forms of BRST symmetry using Batalin-Fradkin-Vilkovisky approach in the case of Abelian 2-form gauge theory. We show that the so-called dual BRST symmetry is not an independent symmetry but the generalization of BRST symmetry obtained from the canonical transformation in the bosonic and ghost sector. We further obtain the new forms of both BRST and dual-BRST symmetry by making a general transformation in the Lagrange multipliers of the bosonic and ghost sector of the theory.
Consequences of an Abelian family symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramond, P.

1996-01-01

The addition of an Abelian family symmetry to the Minimal Super-symmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be sin{sup 2}{theta}{sub {omega}} = 3/8 at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix.
Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

NASA Astrophysics Data System (ADS)

Lee, Taejin

2017-12-01

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.
Interpretation for scales of measurement linking with abstract algebra

PubMed Central

2014-01-01

The Stevens classification of levels of measurement involves four types of scale: “Nominal”, “Ordinal”, “Interval” and “Ratio”. This classification has been used widely in medical fields and has accomplished an important role in composition and interpretation of scale. With this classification, levels of measurements appear organized and validated. However, a group theory-like systematization beckons as an alternative because of its logical consistency and unexceptional applicability in the natural sciences but which may offer great advantages in clinical medicine. According to this viewpoint, the Stevens classification is reformulated within an abstract algebra-like scheme; ‘Abelian modulo additive group’ for “Ordinal scale” accompanied with ‘zero’, ‘Abelian additive group’ for “Interval scale”, and ‘field’ for “Ratio scale”. Furthermore, a vector-like display arranges a mixture of schemes describing the assessment of patient states. With this vector-like notation, data-mining and data-set combination is possible on a higher abstract structure level based upon a hierarchical-cluster form. Using simple examples, we show that operations acting on the corresponding mixed schemes of this display allow for a sophisticated means of classifying, updating, monitoring, and prognosis, where better data mining/data usage and efficacy is expected. PMID:24987515
Lepton mixing patterns from the group Σ (36 ×3 ) with a generalized C P transformation

NASA Astrophysics Data System (ADS)

Rong, Shu-jun

2017-04-01

The group Σ (36 ×3 ) with the generalized C P transformation is introduced to predict the mixing pattern of leptons. Various combinations of Abelian residual flavor symmetries with C P transformations are surveyed. Six mixing patterns could accommodate the fit data of neutrinos oscillation at the 3 σ level. Among them, two patterns predict the nontrivial Dirac C P phase, around ±5 7 ° or ±12 3 ° , which is in accordance with the result of the literature and the recent fit data. Furthermore, one pattern could satisfy the experimental constraints at the 1 σ level.
Topological phases in two-dimensional arrays of parafermionic zero modes

NASA Astrophysics Data System (ADS)

Burrello, M.; van Heck, B.; Cobanera, E.

2013-05-01

It has recently been realized that zero modes with projective non-Abelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a ferromagnet along the edge of a fractional topological insulator (FTI). Here, we study two-dimensional architectures of these non-Abelian zero modes, whose interactions are generated by the charging and Josephson energies of the superconductors. We derive low-energy Hamiltonians for two different arrays of FTIs on the plane, revealing an interesting interplay between the real-space geometry of the system and its topological properties. On the one hand, in a geometry where the length of the FTI edges is independent on the system size, the array has a topologically ordered phase, giving rise to a qudit toric code Hamiltonian in perturbation theory. On the other hand, in a geometry where the length of the edges scales with system size, we find an exact duality to an Abelian lattice gauge theory and no topological order.
Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.

PubMed

Barkeshli, Maissam

2016-08-26

It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1/3 Laughlin FQH state in each layer, with boundaries that are proximity coupled to a superconductor. We show that the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (i) topologically protected degeneracies that can be measured through charge sensing experiments and (ii) a fractional charge 2e/3 ac Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also several generalizations.
Berry phase effect on Majorana braiding

NASA Astrophysics Data System (ADS)

He, Yingping; Wang, Baozong; Liu, Xiong-Jun

Majorana zero modes are predicted to exhibit Non-Abelian braiding, which can be applied to fault-tolerant quantum computation. An essential signature of the non-Abelian braiding is that after a full braiding each of the two Majorana modes under braiding gets a minus sign, namely, a π Berry phase. In this work we find a novel effect in Majorana braiding that during the adiabatic transport a Majorana mode may or may not acquire a staggered minus sign under each step that the Majorana is transported, corresponding to two different types of parameter manipulation. This additional minus sign is shown to be a consequence of translational Berry phase effect, which can qualitatively affect the braiding of Majorana modes. Furthermore, we also study the effect of vortices on the Majorana braiding, with the similar additional Berry phase effect being obtained. Our work may provide new understanding of the non-Abelian statistics of Majorana modes and help improve the experiment setup for quantum computation. MOST, NSFC, Thousand-Young-Talent Program of China.
Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations

NASA Astrophysics Data System (ADS)

Ariznabarreta, Gerardo; García-Ardila, Juan C.; Mañas, Manuel; Marcellán, Francisco

2018-05-01

In this paper, Geronimus–Uvarov perturbations for matrix orthogonal polynomials on the real line are studied and then applied to the analysis of non-Abelian integrable hierarchies. The orthogonality is understood in full generality, i.e. in terms of a nondegenerate continuous sesquilinear form, determined by a quasidefinite matrix of bivariate generalized functions with a well-defined support. We derive Christoffel-type formulas that give the perturbed matrix biorthogonal polynomials and their norms in terms of the original ones. The keystone for this finding is the Gauss–Borel factorization of the Gram matrix. Geronimus–Uvarov transformations are considered in the context of the 2D non-Abelian Toda lattice and noncommutative KP hierarchies. The interplay between transformations and integrable flows is discussed. Miwa shifts, τ-ratio matrix functions and Sato formulas are given. Bilinear identities, involving Geronimus–Uvarov transformations, first for the Baker functions, then secondly for the biorthogonal polynomials and its second kind functions, and finally for the τ-ratio matrix functions, are found.
Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

PubMed

Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

2017-02-24

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.
Dual representation of lattice QCD with worldlines and worldsheets of Abelian color fluxes

NASA Astrophysics Data System (ADS)

Marchis, Carlotta; Gattringer, Christof

2018-02-01

We present a new dual representation for lattice QCD in terms of wordlines and worldsheets. The exact reformulation is carried out using the recently developed Abelian color flux method where the action is decomposed into commuting minimal terms that connect different colors on neighboring sites. Expanding the Boltzmann factors for these commuting terms allows one to reorganize the gauge field contributions according to links such that the gauge fields can be integrated out in closed form. The emerging constraints give the dual variables the structure of worldlines for the fermions and worldsheets for the gauge degrees of freedom. The partition sum has the form of a strong coupling expansion, and with the Abelian color flux approach discussed here all coefficients of the expansion are known in closed form. We present the dual form for three cases: pure SU(3) lattice gauge theory, strong coupling QCD and full QCD, and discuss in detail the constraints for the color fluxes and their physical interpretation.
Faithful actions of locally compact quantum groups on classical spaces

NASA Astrophysics Data System (ADS)

Goswami, Debashish; Roy, Sutanu

2017-07-01

We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

Dynamics of Galaxies in Compact Groups II.

NASA Astrophysics Data System (ADS)

Amram, P.; Mendes de Oliveira, C.

We show partial results of a program based on Fabry-Perot Hα velocity field data of compact groups taken at the ESO and the CFH 3.6m telescopes in order to analyze the kinematics of compact group galaxies. This project has three main goals: 1. determine the evolutionary stages of the groups; 2. search for tidal dwarf galaxies and 3. determine the Tully-Fisher relation for the group galaxies. We classify the compact groups studied so far into the following subclasses : (1) merging groups, (2) strongly interacting, (3) mildly interacting, (4) kinematically undisturbed and (5) false groups/single galaxy (details are given in the companion paper Mendes de Oliveira and Amram, 2000). We present examples of velocity fields of galaxies in compact groups that are in different evolutionary stages as classified from the kinematic disturbances. Spiral-only groups have often been considered chance alignments or groups in the very early stages of dynamical evolution. However, we find that the kinematics of the member galaxies for spiral-only groups in classes (1), (2) and (3) above display peculiarities which suggest that the galaxies know of the presence of their neighbors.
Constructing the quantum Hall system on the Grassmannians Gr2(CN)

NASA Astrophysics Data System (ADS)

Ballı, F.; Behtash, A.; Kürkçüoğlu, S.; Ünal, G.

2015-04-01

In this talk, we give the formulation of Quantum Hall Effects (QHEs) on the complex Grassmann manifolds Gr2(CN). We set up the Landau problem in Gr2(CN), solve it using group theoretical techniques and provide the energy spectrum and the eigenstates in terms of the SU(N) Wigner D-functions for charged particles on Gr2(CN) under the influence of abelian and non-abelian background magnetic monopoles or a combination of these thereof. For the simplest case of Gr2(C4) we provide explicit constructions of the single and many- particle wavefunctions by introducing the Plucker coordinates and show by calculating the two-point correlation function that the lowest Landau level (LLL) at filling factor v = 1 forms an incompressible fluid. Finally, we heuristically identify a relation between the U(1) Hall effect on Gr2(C4) and the Hall effect on the odd sphere S5, which is yet to be investigated in detail, by appealing to the already known analogous relations between the Hall effects on CP3 and CP7 and those on the spheres S4 and S8, respectively. The talk is given by S. Kürkçüoğlu at the Group 30 meeting at Ghent University, Ghent, Belgium in July 2014 and based on the article by F.Ballı, A.Behtash, S. Kürkçüoğlu, G.Ünal [1].
Free Quantum Field Theory from Quantum Cellular Automata

NASA Astrophysics Data System (ADS)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro

2015-10-01

After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Hi Image Synthesis of Southern Compact Groups

NASA Astrophysics Data System (ADS)

Babic, B.; Price, R. M.; Jones, K.

Four southern compact groups, the Hickson Compact Groups HCG 22 and HCG 26 (Hickson 1982), and the groups AM 1238 - 396 and ESO 410-G(024 - 026) have been imaged in Hi, along with 12 cm continuum using the Australia Telescope Compact Array (ATCA). The initial findings for the latter two groups are presented here. While ESO 410-G is not in fact a physical group, due to the discordant redshifts amongst the members, it is however presented here. Overall for all the groups we find no other sources of Hi in the field that might indicate that these are part of a larger loose group structure. This is not always the case, as with HCG 23 (Williams 1995) and HCG 95 (Hutchmeier 1999), both of whom find additional Hi sources within the primary beam accordant with the compact group's velocity. The Hi is also clearly associated with each of the individual member galaxies in all cases, except for HCG 26, which envelopes the whole group as was also shown by Williams and van Gorkom (Williams 1995).
Mimetic discretization of the Abelian Chern-Simons theory and link invariants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Einstein-Yang-Mills-Dirac systems from the discretized Kaluza-Klein theory

NASA Astrophysics Data System (ADS)

Wali, Kameshwar; Viet, Nguyen Ali

2017-01-01

A unified theory of the non-Abelian gauge interactions with gravity in the framework of a discretized Kaluza-Klein theory is constructed with a modified Dirac operator and wedge product. All the couplings of chiral spinors to the non-Abelian gauge fields emerge naturally as components of the coupling of the chiral spinors in the generalized gravity together with some new interactions. In particular, the currently prevailing gravity-QCD quark and gravity-electroweak-quark and lepton models are shown to follow as special cases of the general framework.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants

NASA Astrophysics Data System (ADS)

Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo

2013-12-01

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.
Holography in Lovelock Chern-Simons AdS gravity

NASA Astrophysics Data System (ADS)

Cvetković, Branislav; Miskovic, Olivera; Simić, Dejan

2017-08-01

We analyze holographic field theory dual to Lovelock Chern-Simons anti-de Sitter (AdS) gravity in higher dimensions using first order formalism. We first find asymptotic symmetries in the AdS sector showing that they consist of local translations, local Lorentz rotations, dilatations and non-Abelian gauge transformations. Then, we compute 1-point functions of energy-momentum and spin currents in a dual conformal field theory and write Ward identities. We find that the holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge symmetry at the quantum level.
Wigner functions for noncommutative quantum mechanics: A group representation based construction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.« less
Non-Abelian clouds around Reissner-Nordström black holes: The existence line

NASA Astrophysics Data System (ADS)

Radu, Eugen; Tchrakian, D. H.; Yang, Yisong

2016-06-01

A known feature of electrically charged Reissner-Nordström-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein-Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordström (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisites for the existence of the nA clouds are (i) a large enough gauge group, and (ii) the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four- and the other in five-dimensional asymptotically flat spacetime. In the first case, we augment the usual S U (3 ) Yang-Mills Lagrangian with a higher-order (quartic) curvature term, while for the second one we add the Chern-Simons density to the S O (6 ) Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity.
The birthplace of compact groups of galaxies

NASA Technical Reports Server (NTRS)

Ramella, Massimo; Diaferio, Antonaldo; Geller, Margaret J.; Huchra, John P.

1994-01-01

We use complete redshift surveys to study the redshift neighborhoods of 38 Hickson compact groups (HCGs). Twenty-nine of these HCGs (76%) are embedded in rich looser systems which we call HCG associations. Analysis of the redshift neighborhood of HCGs outside the CfA survey suggests that most HCGs are embedded in more extended physical systems. Rich loose groups extracted from the CfA survey (Ramella et al. (1994)) have physical properties similar to those of the HCG associations. These rich loose groups often contain compact configurations. N-body experiments (Diaferio (1994)) suggest that compact configurations analogous to HCGs form continually during the collapse of rich loose groups. These observational and numerical results suggest that rich loose groups are the birthplace of HCGs.
Aspects Topologiques de la Theorie des Champs et leurs Applications

NASA Astrophysics Data System (ADS)

Caenepeel, Didier

This thesis is dedicated to the study of various topological aspects of field theory, and is divided in three parts. In two space dimensions the possibility of fractional statistics can be implemented by adding an appropriate "fictitious" electric charge and magnetic flux to each particle (after which they are known as anyons). Since the statistical interaction is rather difficult to handle, a mean-field approximation is used in order to describe a gas of anyons. We derive a criterion for the validity of this approximation using the inherent feature of parity violation in the scattering of anyons. We use this new method in various examples of anyons and show both analytically and numerically that the approximation is justified if the statistical interaction is weak, and that it must be more weak for boson-based than for fermion-based anyons. Chern-Simons theories give an elegant implementation of anyonic properties in field theories, which permits the emergence of new mechanisms for anyon superconductivity. Since it is reasonable to think that superconductivity is a low energy phenomenon, we have been interested in non-relativistic C-S systems. We present the scalar field effective potential for non-relativistic matter coupled to both Abelian and non-Abelian C-S gauge fields. We perform the calculations using functional methods in background fields. Finally, we compute the scalar effective potential in various gauges and treat divergences with various regularization schemes. In three space dimensions, a generalization of Chern-Simons theory may be achieved by introducing an antisymmetric tensor gauge field. We use these theories, called B wedge F theories, to present an alternative to the Higgs mechanism to generate masses for non-Abelian gauge fields. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self -interactions minimally coupled to non-Abelian gauge fields. The mass generation occurs upon the fermionic functional integration. We show that by suitably adjusting the coupling constants the effective theory contains massive non-Abelian gauge fields without any residual scalars or other degrees of freedom.
Noncommutative gauge theories and Kontsevich's formality theorem

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schupp, P.; Wess, J.

2001-09-01

The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a "Mini Seiberg-Witten map" that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor.
Duality in a supersymmetric gauge theory from a perturbative viewpoint

NASA Astrophysics Data System (ADS)

Ryttov, Thomas A.; Shrock, Robert

2018-03-01

We study duality in N =1 supersymmetric QCD in the non-Abelian Coulomb phase, order-by-order in scheme-independent series expansions. Using exact results, we show how the dimensions of various fundamental and composite chiral superfields, and the quantities a , c , a /c , and b at superconformal fixed points of the renormalization group emerge in scheme-independent series expansions in the electric and magnetic theories. We further demonstrate that truncations of these series expansions to modest order yield very accurate approximations to these quantities and suggest possible implications for nonsupersymmetric theories.
Physically detached 'compact groups'

NASA Technical Reports Server (NTRS)

Hernquist, Lars; Katz, Neal; Weinberg, David H.

1995-01-01

A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement among researchers attempting to deduce the dynamical state of these systems. In this paper, we suggest that many of the observed groups are not physically bound but are chance projections of galaxies well separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be members of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is nonnegligible if most galaxies are distributed in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections is sufficient, in principle, to explain the observed space density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.
Semistrict higher gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Sämann, Christian; Wolf, Martin

2015-04-01

We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Čech groupoid to weak Lie 2-groups. As is demonstrated, some of these Lie 2-groups can be differentiated to semistrict Lie 2-algebras by a method due to Ševera. We further derive the full description of connective structures on semistrict principal 2-bundles including the non-linear gauge transformations. As an application, we use a twistor construction to derive superconformal constraint equations in six dimensions for a non-Abelian tensor multiplet taking values in a semistrict Lie 2-algebra.
On spectroscopy for a whole Abelian model

NASA Astrophysics Data System (ADS)

Chauca, J.; Doria, R.

2012-10-01

Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemic gauge symmetry. Now, it introduces a fields set {AμI} rotating under a common gauge symmetry. Thus, given a fields collection {AμI} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.
The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua

NASA Astrophysics Data System (ADS)

Weigand, Timo; Xu, Fengjun

2018-04-01

We study the structure of gauge and gravitational anomalies in 2d N = (0 , 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1 , 0) and 4d N = 1 theories obtained from F-theory.
Some novel features in 2D non-Abelian theory: BRST approach

NASA Astrophysics Data System (ADS)

Srinivas, N.; Kumar, S.; Kureel, B. K.; Malik, R. P.

2017-08-01

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF-)type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.
Solitons, τ-functions and hamiltonian reduction for non-Abelian conformal affine Toda theories

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Miramontes, J. Luis; Guillén, Joaquín Sánchez

1995-02-01

We consider the Hamiltonian reduction of the "two-loop" Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody algebra G. The resulting reduced models, called Generalized Non-Abelian Conformal Affine Toda (G-CAT), are conformally invariant and a wide class of them possesses soliton solutions; these models constitute non-Abelian generalizations of the conformal affine Toda models. Their general solution is constructed by the Leznov-Saveliev method. Moreover, the dressing transformations leading to the solutions in the orbit of the vacuum are considered in detail, as well as the τ-functions, which are defined for any integrable highest weight representation of G, irrespectively of its particular realization. When the conformal symmetry is spontaneously broken, the G-CAT model becomes a generalized affine Toda model, whose soliton solutions are constructed. Their masses are obtained exploring the spontaneous breakdown of the conformal symmetry, and their relation to the fundamental particle masses is discussed. We also introduce what we call the two-loop Virasoro algebra, describing extended symmetries of the two-loop WZNW models.

Abelian Toda field theories on the noncommutative plane

NASA Astrophysics Data System (ADS)

Cabrera-Carnero, Iraida

2005-10-01

Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.
Non-Abelian fractional quantum Hall states for hard-core bosons in one dimension

NASA Astrophysics Data System (ADS)

Paredes, Belén

2012-05-01

I present a family of one-dimensional bosonic liquids analogous to non-Abelian fractional quantum Hall states. A new quantum number is introduced to characterize these liquids, the chiral momentum, which differs from the usual angular or linear momentum in one dimension. As their two-dimensional counterparts, these liquids minimize a k-body hard-core interaction with the minimum total chiral momentum. They exhibit global order, with a hidden organization of the particles in k identical copies of a one-dimensional Laughlin state. For k=2 the state is a p-wave paired phase corresponding to the Pfaffian quantum Hall state. By imposing conservation of the total chiral momentum, an exact parent Hamiltonian is derived which involves long-range tunneling and interaction processes with an amplitude decaying with the chord distance. This family of non-Abelian liquids is shown to be in formal correspondence with a family of spin-(k)/(2) liquids which are total singlets made out of k indistinguishable resonating valence bond states. The corresponding spin Hamiltonians are obtained.
Blue ellipticals in compact groups

NASA Technical Reports Server (NTRS)

Zepf, Stephen E.; Whitmore, Bradley C.

1990-01-01

By studying galaxies in compact groups, the authors examine the hypothesis that mergers of spiral galaxies make elliptical galaxies. The authors combine dynamical models of the merger-rich compact group environment with stellar evolution models and predict that roughly 15 percent of compact group ellipticals should be 0.15 mag bluer in B - R color than normal ellipticals. The published colors of these galaxies suggest the existence of this predicted blue population, but a normal distribution with large random errors can not be ruled out based on these data alone. However, the authors have new ultraviolet blue visual data which confirm the blue color of the two ellipticals with blue B - R colors for which they have their own colors. This confirmation of a population of blue ellipticals indicates that interactions are occurring in compact groups, but a blue color in one index alone does not require that these ellipticals are recent products of the merger of two spirals. The authors demonstrate how optical spectroscopy in the blue may distinguish between a true spiral + spiral merger and the swallowing of a gas-rich system by an already formed elliptical. The authors also show that the sum of the luminosity of the galaxies in each group is consistent with the hypothesis that the final stage in the evolution of compact group is an elliptical galaxy.
Theory of the disordered ν =5/2 quantum thermal Hall state: Emergent symmetry and phase diagram

NASA Astrophysics Data System (ADS)

Lian, Biao; Wang, Juven

2018-04-01

Fractional quantum Hall (FQH) system at Landau level filling fraction ν =5 /2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σx y=5 e2/2 h . Thermal Hall conductances of the Pf and APf states are quantized at κx y=7 /2 and κx y=3 /2 , respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν =5 /2 FQH state is κx y=5 /2 . It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κx y=5 /2 phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ1, which is lowered to an emergent U (1 )×U (1) symmetry at energy scales between Λ1 and a higher value Λ2, and is finally lowered to the composite fermion parity symmetry Z2F above Λ2. Based on the emergent symmetries, we propose a phase diagram of the disordered ν =5 /2 FQH system and show that a κx y=5 /2 phase arises at disorder energy scales Λ >Λ1 . Furthermore, we show the gapped double-semion sector of ND compact domain walls contributes nonlocal topological degeneracy 2ND-1, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological 1 +1 D domain walls (two-surface defects) applicable to any 2 +1 D non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various ν =5 /2 FQH states in terms of fermionic version of U (1) ±8 Chern-Simons theory ×Z8 -class TQFTs.
Berry phases for Landau Hamiltonians on deformed tori

NASA Astrophysics Data System (ADS)

Lévay, Péter

1995-06-01

Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γϑ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γϑ the geodesic motion restricted to the fundamental domain of this group is chaotic.
A minimal model of neutrino flavor

NASA Astrophysics Data System (ADS)

Luhn, Christoph; Parattu, Krishna Mohan; Wingerter, Akın

2012-12-01

Models of neutrino mass which attempt to describe the observed lepton mixing pattern are typically based on discrete family symmetries with a non-Abelian and one or more Abelian factors. The latter so-called shaping symmetries are imposed in order to yield a realistic phenomenology by forbidding unwanted operators. Here we propose a supersymmetric model of neutrino flavor which is based on the group T 7 and does not require extra {Z} N or U(1) factors in the Yukawa sector, which makes it the smallest realistic family symmetry that has been considered so far. At leading order, the model predicts tribimaximal mixing which arises completely accidentally from a combination of the T 7 Clebsch-Gordan coefficients and suitable flavon alignments. Next-to-leading order (NLO) operators break the simple tribimaximal structure and render the model compatible with the recent results of the Daya Bay and Reno collaborations which have measured a reactor angle of around 9°. Problematic NLO deviations of the other two mixing angles can be controlled in an ultraviolet completion of the model. The vacuum alignment mechanism that we use necessitates the introduction of a hidden flavon sector that transforms under a {Z} 6 symmetry, thereby spoiling the minimality of our model whose flavor symmetry is then T 7 × {Z} 6.
Localization Protection and Symmetry Breaking in One-dimensional Potts Chains

NASA Astrophysics Data System (ADS)

Friedman, Aaron; Vasseur, Romain; Potter, Andrew; Parameswaran, Siddharth

Recent work on the 3-state Potts and Z3 clock models has demonstrated that their ordered phases are connected by duality to a phase that hosts topologically protected parafermionic zero modes at the system's boundary. The analogy with Kitaev's example of the one-dimensional Majorana chain (similarly related by duality to the Ising model) suggests that such zero modes may also be stabilized in highly excited states by many-body localization (MBL). However, the Potts model has a non-Abelian S3 symmetry believed to be incompatible with MBL; hence any MBL state must spontaneously break this symmetry, either completely or into one of its abelian subgroups (Z2 or Z3), with the topological phase corresponding to broken Z3 symmetry. We therefore study the excited state phase structure of random three-state Potts and clock models in one dimension using exact diagonalization and real-space renormalization group techniques. We also investigate the interesting possibility of a direct excited-state transition between MBL phases that break either Z3 or Z2 symmetry, forbidden within Landau theory. NSF DGE-1321846 (AJF), NSF DMR-1455366 and President's Research Catalyst Award No. CA-15-327861 from the University of California Office of the President (SAP), LDRD Program of LBNL (RV), NSF PHY11-25915 at the KITP (AJF, RV, SAP).
Non-Abelian cosmic string in the Starobinsky model of gravity

NASA Astrophysics Data System (ADS)

Morais Graça, J. P.; de Pádua Santos, A.; Bezerra de Mello, Eugênio R.; Bezerra, V. B.

In this paper, we analyze numerically the behavior of the solutions corresponding to a non-Abelian cosmic string in the framework of the Starobinsky model, i.e. where f(R) = R + ζR2. We perform the calculations for both an asymptotically flat and asymptotically (anti)-de Sitter spacetimes. We found that the angular deficit generated by the string decreases as the parameter ζ increases, in the case of a null cosmological constant. For a positive cosmological constant, we found that the cosmic horizon is affected in a nontrivial way by the parameter ζ.
Extended gauge theory and gauged free differential algebras

NASA Astrophysics Data System (ADS)

Salgado, P.; Salgado, S.

2018-01-01

Recently, Antoniadis, Konitopoulos and Savvidy introduced, in the context of the so-called extended gauge theory, a procedure to construct background-free gauge invariants, using non-abelian gauge potentials described by higher degree forms. In this article it is shown that the extended invariants found by Antoniadis, Konitopoulos and Savvidy can be constructed from an algebraic structure known as free differential algebra. In other words, we show that the above mentioned non-abelian gauge theory, where the gauge fields are described by p-forms with p ≥ 2, can be obtained by gauging free differential algebras.
Abelian-Higgs phase of SU(2) QCD and glueball energy

NASA Astrophysics Data System (ADS)

Jia, Duojie

2008-07-01

It is shown that SU(2) QCD admits an dual Abelian-Higgs phase, with a Higgs vacuum of a type-II superconductor. This is done by using a connection decomposition for the gluon field and the random-direction approximation. Using a bag picture with soft wall, we presented a calculational procedure for the glueball energy based on the recent proof for wall-vortices [Nucl. Phys. B 741(2006)1]. Supported by National Natural Science Foundation of China (10547009) and Research Backbone Fostering Program of Knowledge and S&T Innovation Project of NWNU (KJCXGC 03-41)
Explaining compact groups as change alignments

NASA Technical Reports Server (NTRS)

Mamon, Gary A.

1990-01-01

The physical nature of the apparently densest groups of galaxies, known as compact groups is a topic of some recent controversy, despite the detailed observations of a well-defined catalog of 100 isolated compact groups compiled by Hickson (1982). Whereas many authors have espoused the view that compact groups are bound systems, typically as dense as they appear in projection on the sky (e.g., Williams & Rood 1987; Sulentic 1987; Hickson & Rood 1988), others see them as the result of chance configurations within larger systems, either in 1D (chance alignments: Mamon 1986; Walke & Mamon 1989), or in 3D (transient cores: Rose 1979). As outlined in the companion review to this contribution (Mamon, in these proceedings), the implication of Hickson's compact groups (HCGs) being dense bound systems is that they would then constitute the densest isolated systems of galaxies in the Universe and the privileged site for galaxy interactions. In a previous paper (Mamon 1986), the author reviewed the arguments given for the different theories of compact groups. Since then, a dozen papers have been published on the subject, including a thorough and perceptive review by White (1990), thus more than doubling the amount written on the subject. Here, the author first enumerates the arguments that he brought up in 1986 substantiating the chance alignment hypothesis, then he reviews the current status of the numerous recent arguments arguing against chance alignments and/or for the bound dense group hypothesis (both for the majority of HCGs but not all of them), and finally he reconsiders each one of these anti-chance alignment arguments and shows that, rather than being discredited, the chance alignment hypothesis remains a fully consistent explanation for the nature of compact groups.
Quantum non-Abelian hydrodynamics: Anyonic or spin-orbital entangled liquids, nonunitarity of scattering matrix and charge fractionalization

NASA Astrophysics Data System (ADS)

Pareek, Tribhuvan Prasad

2015-09-01

In this article, we develop an exact (nonadiabatic, nonperturbative) density matrix scattering theory for a two component quantum liquid which interacts or scatters off from a generic spin-dependent quantum potential. The generic spin dependent quantum potential [Eq. (1)] is a matrix potential, hence, adiabaticity criterion is ill-defined. Therefore the full matrix potential should be treated nonadiabatically. We succeed in doing so using the notion of vectorial matrices which allows us to obtain an exact analytical expression for the scattered density matrix (SDM), ϱsc [Eq. (30)]. We find that the number or charge density in scattered fluid, Tr(ϱsc), expressions in Eqs. (32) depends on nontrivial quantum interference coefficients, Qα β 0ijk, which arises due to quantum interference between spin-independent and spin-dependent scattering amplitudes and among spin-dependent scattering amplitudes. Further it is shown that Tr(ϱsc) can be expressed in a compact form [Eq. (39)] where the effect of quantum interference coefficients can be included using a vector Qαβ, which allows us to define a vector order parameterQ. Since the number density is obtained using an exact scattered density matrix, therefore, we do not need to prove that Q is non-zero. However, for sake of completeness, we make detailed mathematical analysis for the conditions under which the vector order parameterQ would be zero or nonzero. We find that in presence of spin-dependent interaction the vector order parameterQ is necessarily nonzero and is related to the commutator and anti-commutator of scattering matrix S with its dagger S† [Eq. (78)]. It is further shown that Q≠0, implies four physically equivalent conditions,i.e., spin-orbital entanglement is nonzero, non-Abelian scattering phase, i.e., matrices, scattering matrix is nonunitary and the broken time reversal symmetry for SDM. This also implies that quasi particle excitation are anyonic in nature, hence, charge fractionalization is a natural consequence. This aspect has also been discussed from the perspective of number or charge density conservation, which implies i.e., Tr(ϱ} sc) = Tr(ϱin). On the other hand Q = 0 turns out to be a mathematically forced unphysical solution in presence of spin-dependent potential or scattering which is equivalent to Abelian hydrodynamics, unitary scattering matrix, absence of spin-space entanglement and preserved time reversal symmetry. We have formulated the theory using mesoscopic language, specifically, we have considered two terminal systems connected to spin-dependent scattering region, which is equivalent to having two potential wells separated by a generic spin-dependent potential barrier. The formulation using mesoscopic language is practically useful because it leads directly to the measured quantities such as conductance and spin-polarization density in the leads, however, the presented formulation is not limited to the mesoscopic system only, its generality has been stressed at various places in this article.
Examining the Role of Environment in a Comprehensive Sample of Compact Groups

NASA Astrophysics Data System (ADS)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.

2012-03-01

Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant "gap" has been discovered in the mid-infrared (MIR: 3.6-8 μm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been pre-selected to be compact and dense. Thus, the relative influence of stochastic effects (such as the particular distribution and amount of star formation in individual galaxies) becomes dominant. We analyze spectral energy distributions of member galaxies as a function of their location in color space and find that galaxies in different regions of MIR color space contain dust with varying temperatures and/or polycyclic aromatic hydrocarbon emission.
Examining the Role of Environment in a Comprehensive Sample of Compact Groups

NASA Technical Reports Server (NTRS)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.; Charlton, Jane C.; Hornschemeier, Ann E.; Hibbard, John E.

2012-01-01

Compact groups, with their high number densities, small velocity dispersions, and an interstellar medium that has not been fully processed, provide a local analog to conditions of galaxy interactions in the earlier universe. The frequent and prolonged gravitational encounters that occur in compact groups affect the evolution of the constituent galaxies in a myriad of ways, for example, gas processing and star formation. Recently, a statistically significant "gap" has been discovered in the mid-infrared (MIR: 3.6-8 µm) IRAC color space of compact group galaxies. This gap is not seen in field samples and is a new example of how the compact group environment may affect the evolution of member galaxies. In order to investigate the origin and nature of this gap, we have compiled a larger sample of 37 compact groups in addition to the original 12 groups studied by Johnson et al. (yielding 174 individual galaxies with reliable MIR photometry). We find that a statistically significant deficit of galaxies in this gap region of IRAC color space is persistent in the full sample, lending support to the hypothesis that the compact group environment inhibits moderate specific star formation rates. Using this expanded sample, we have more fully characterized the distribution of galaxies in this color space and quantified the low-density region more fully with respect to MIR bluer and MIR redder colors. We note a curvature in the color-space distribution, which is fully consistent with increasing dust temperature as the activity in a galaxy increases. This full sample of 49 compact groups allows us to subdivide the data according to physical properties of the groups. An analysis of these subsamples indicates that neither projected physical diameter nor density shows a trend in color space within the values represented by this sample. We hypothesize that the apparent lack of a trend is due to the relatively small range of properties in this sample, whose groups have already been pre-selected to be compact and dense. Thus, the relative influence of stochastic effects (such as the particular distribution and amount of star formation in individual galaxies) becomes dominant. We analyze spectral energy distributions of member galaxies as a function of their location in color space and find that galaxies in different regions of MIR color space contain dust with varying temperatures and/or polycyclic aromatic hydrocarbon emission.
Trust and compactness in social network groups.

PubMed

De Meo, Pasquale; Ferrara, Emilio; Rosaci, Domenico; Sarné, Giuseppe M L

2015-02-01

Understanding the dynamics behind group formation and evolution in social networks is considered an instrumental milestone to better describe how individuals gather and form communities, how they enjoy and share the platform contents, how they are driven by their preferences/tastes, and how their behaviors are influenced by peers. In this context, the notion of compactness of a social group is particularly relevant. While the literature usually refers to compactness as a measure to merely determine how much members of a group are similar among each other, we argue that the mutual trustworthiness between the members should be considered as an important factor in defining such a term. In fact, trust has profound effects on the dynamics of group formation and their evolution: individuals are more likely to join with and stay in a group if they can trust other group members. In this paper, we propose a quantitative measure of group compactness that takes into account both the similarity and the trustworthiness among users, and we present an algorithm to optimize such a measure. We provide empirical results, obtained from the real social networks EPINIONS and CIAO, that compare our notion of compactness versus the traditional notion of user similarity, clearly proving the advantages of our approach.
The Collaborative Compact: Operating Principles Lay the Groundwork for Successful Group Work

ERIC Educational Resources Information Center

Garmston, Robert J.; Zimmerman, Diane P.

2013-01-01

Leaders often have common complaints about managing meetings and feel thwarted by attempts to collaborate. Teachers feel that time spent on collaboration is often wasted because of poor meeting management. Leaders can accelerate collaboration by creating collaborative compacts. A collaborative compact is a set of accords about how a group will…
The Ultraviolet and Infrared Star Formation Rates of Compact Group Galaxies: An Expanded Sample

NASA Technical Reports Server (NTRS)

Lenkic, Laura; Tzanavaris, Panayiotis; Gallagher, Sarah C.; Desjardins, Tyler D.; Walker, Lisa May; Johnson, Kelsey E.; Fedotov, Konstantin; Charlton, Jane; Cardiff, Ann H.; Durell, Pat R.

2016-01-01

Compact groups of galaxies provide insight into the role of low-mass, dense environments in galaxy evolution because the low velocity dispersions and close proximity of galaxy members result in frequent interactions that take place over extended time-scales. We expand the census of star formation in compact group galaxies by Tzanavaris et al. (2010) and collaborators with Swift UVOT, Spitzer IRAC and MIPS 24 m photometry of a sample of 183 galaxies in 46 compact groups. After correcting luminosities for the contribution from old stellar populations, we estimate the dust-unobscured star formation rate (SFRUV) using the UVOT uvw2 photometry. Similarly, we use the MIPS 24 m photometry to estimate the component of the SFR that is obscured by dust (SFRIR). We find that galaxies which are MIR-active (MIR-red), also have bluer UV colours, higher specific SFRs, and tend to lie in Hi-rich groups, while galaxies that are MIR-inactive (MIR-blue) have redder UV colours, lower specific SFRs, and tend to lie in Hi-poor groups. We find the SFRs to be continuously distributed with a peak at about 1 M yr1, indicating this might be the most common value in compact groups. In contrast, the specific SFR distribution is bimodal, and there is a clear distinction between star-forming and quiescent galaxies. Overall, our results suggest that the specific SFR is the best tracer of gas depletion and galaxy evolution in compact groups.
ROSAT observations of compact groups of galaxies

NASA Technical Reports Server (NTRS)

Pildis, Rachel A.; Bregman, Joel N.; Evrard, August E.

1995-01-01

We have systematically analyzed a sample of 13 new and archival ROSAT Position Sensitive Proportional Counter (PSPC) observations of compact groups of galaxies: 12 Hickson compact groups plus the NCG 2300 group. We find that approximately two-thirds of the groups have extended X-ray emission and, in four of these, the emission is resolved into diffuse emission from gas at a temperature of kT approximately 1 keV in the group potential. All but one of the groups with extended emission have a spiral fraction of less than 50%. The baryon fraction of groups with diffuse emission is 5%-19%, similar to the values in clusters of galaxies. However, with a single exception (HCG 62), the gas-to-stellar mass ratio in our groups has a median value near 5%, somewhat greater than the values for individual early-type galaxies and two orders of magnitude than in clusters of galaxies. The X-ray luminosities of individual group galaxies are comparable to those of similar field galaxies, although the L(sub X)-L(sub B) relation for early-type galaxies may be flatter in compact groups than in the field.
Quasi-periodic solutions to nonlinear beam equations on compact Lie groups with a multiplicative potential

NASA Astrophysics Data System (ADS)

Chen, Bochao; Gao, Yixian; Jiang, Shan; Li, Yong

2018-06-01

The goal of this work is to study the existence of quasi-periodic solutions to nonlinear beam equations with a multiplicative potential. The nonlinearity is required to only finitely differentiable and the frequency is along a pre-assigned direction. The result holds on any compact Lie group or homogeneous manifold with respect to a compact Lie group, which includes standard torus Td, special orthogonal group SO (d), special unitary group SU (d), spheres Sd and the real and complex Grassmannians. The proof is based on a differentiable Nash-Moser iteration scheme.
Geometric Defects in Quantum Hall States

NASA Astrophysics Data System (ADS)

Gromov, Andrey

I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.

Rotating black holes with non-Abelian hair

NASA Astrophysics Data System (ADS)

Kleihaus, Burkhard; Kunz, Jutta; Navarro-Lérida, Francisco

2016-12-01

We here review asymptotically flat rotating black holes in the presence of non-Abelian gauge fields. Like their static counterparts these black holes are no longer uniquely determined by their global charges. In the case of pure SU(2) Yang-Mills fields, the rotation generically induces an electric charge, while the black holes do not carry a magnetic charge. When a Higgs field is coupled, rotating black holes with monopole hair arise in the case of a Higgs triplet, while in the presence of a complex Higgs doublet the black holes carry sphaleron hair. The inclusion of a dilaton allows for Smarr type mass formulae.
Symplectic analysis of three-dimensional Abelian topological gravity

NASA Astrophysics Data System (ADS)

Cartas-Fuentevilla, R.; Escalante, Alberto; Herrera-Aguilar, Alfredo

2017-02-01

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; we show that this formalism is equivalent and more economical than Dirac's method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide with each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.
Bosonization of fermions coupled to topologically massive gravity

NASA Astrophysics Data System (ADS)

Fradkin, Eduardo; Moreno, Enrique F.; Schaposnik, Fidel A.

2014-03-01

We establish a duality between massive fermions coupled to topologically massive gravity (TMG) in d=3 space-time dimensions and a purely gravity theory which also will turn out to be a TMG theory but with different parameters: the original graviton mass in the TMG theory coupled to fermions picks up a contribution from fermion bosonization. We obtain explicit bosonization rules for the fermionic currents and for the energy-momentum tensor showing that the identifications do not depend explicitly on the parameters of the theory. These results are the gravitational analog of the results for 2+1 Abelian and non-Abelian bosonization in flat space-time.
Enhanced Bulk-Edge Coulomb Coupling in Fractional Fabry-Perot Interferometers.

PubMed

von Keyserlingk, C W; Simon, S H; Rosenow, Bernd

2015-09-18

Recent experiments use Fabry-Perot (FP) interferometry to claim that the ν=5/2 quantum Hall state exhibits non-Abelian topological order. We note that the experiments appear inconsistent with a model neglecting bulk-edge Coulomb coupling and Majorana tunneling, so we reexamine the theory of FP devices. Even a moderate Coulomb coupling may strongly affect some fractional plateaus, but very weakly affect others, allowing us to model the data over a wide range of plateaus. While experiments are consistent with the ν=5/2 state harboring Moore-Read topological order, they may have measured Coulomb effects rather than an "even-odd effect" due to non-Abelian braiding.
Establishing non-Abelian topological order in Gutzwiller-projected Chern insulators via entanglement entropy and modular S-matrix

NASA Astrophysics Data System (ADS)

Zhang, Yi; Vishwanath, Ashvin

2013-04-01

We use entanglement entropy signatures to establish non-Abelian topological order in projected Chern-insulator wave functions. The simplest instance is obtained by Gutzwiller projecting a filled band with Chern number C=2, whose wave function may also be viewed as the square of the Slater determinant of a band insulator. We demonstrate that this wave function is captured by the SU(2)2 Chern-Simons theory coupled to fermions. This is established most persuasively by calculating the modular S-matrix from the candidate ground-state wave functions, following a recent entanglement-entropy-based approach. This directly demonstrates the peculiar non-Abelian braiding statistics of Majorana fermion quasiparticles in this state. We also provide microscopic evidence for the field theoretic generalization, that the Nth power of a Chern number C Slater determinant realizes the topological order of the SU(N)C Chern-Simons theory coupled to fermions, by studying the SU(2)3 (Read-Rezayi-type state) and the SU(3)2 wave functions. An advantage of our projected Chern-insulator wave functions is the relative ease with which physical properties, such as entanglement entropy and modular S-matrix, can be numerically calculated using Monte Carlo techniques.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms

NASA Astrophysics Data System (ADS)

Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan

2014-08-01

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a ``hairline'' solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms.

PubMed

Huo, Ming-Xia; Nie, Wei; Hutchinson, David A W; Kwek, Leong Chuan

2014-08-08

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a "hairline" solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions.
Open/closed string duality and relativistic fluids

NASA Astrophysics Data System (ADS)

Niarchos, Vasilis

2016-07-01

We propose an open/closed string duality in general backgrounds extending previous ideas about open string completeness by Ashoke Sen. Our proposal sets up a general version of holography that works in gravity as a tomographic principle. We argue, in particular, that previous expectations of a supergravity/Dirac-Born-Infeld (DBI) correspondence are naturally embedded in this conjecture and can be tested in a well-defined manner. As an example, we consider the correspondence between open string field theories on extremal D-brane setups in flat space in the large-N , large 't Hooft limit, and asymptotically flat solutions in ten-dimensional type II supergravity. We focus on a convenient long-wavelength regime, where specific effects of higher-spin open string modes can be traced explicitly in the dual supergravity computation. For instance, in this regime we show how the full Abelian DBI action arises from supergravity as a straightforward reformulation of relativistic hydrodynamics. In the example of a (2 +1 )-dimensional open string theory this reformulation involves an Abelian Hodge duality. We also point out how different deformations of the DBI action, related to higher-derivative corrections and non-Abelian effects, can arise in this context as deformations in corresponding relativistic hydrodynamics.
Non-Abelian black string solutions of N = (2,0) , d = 6 supergravity

NASA Astrophysics Data System (ADS)

Cano, Pablo A.; Ortín, Tomás; Santoli, Camilla

2016-12-01

We show that, when compactified on a circle, N = (2, 0), d = 6 supergravity coupled to 1 tensor multiplet and n V vector multiplets is dual to N = (2 , 0) , d = 6 supergravity coupled to just n T = n V + 1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N = 2 , d = 5 supergravity coupled to n V 5 = n V + 2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N = 2 , d = 5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions, similar to the gauge dyonic string of Duff, Lü and Pope. One of the solutions obtained interpolates smoothly between two AdS3× S3 geometries with different radii.
Cosmological bounds on non-Abelian dark forces

NASA Astrophysics Data System (ADS)

Forestell, Lindsay; Morrissey, David E.; Sigurdson, Kris

2018-04-01

Non-Abelian dark gauge forces that do not couple directly to ordinary matter may be realized in nature. The minimal form of such a dark force is a pure Yang-Mills theory. If the dark sector is reheated in the early Universe, it will be realized as a set of dark gluons at high temperatures and as a collection of dark glueballs at lower temperatures, with a cosmological phase transition from one form to the other. Despite being dark, the gauge fields of the new force can connect indirectly to the standard model through nonrenormalizable operators. These operators will transfer energy between the dark and visible sectors, and they allow some or all of the dark glueballs to decay. In this work we investigate the cosmological evolution and decays of dark glueballs in the presence of connector operators to the standard model. Dark glueball decays can modify cosmological and astrophysical observables, and we use these considerations to put very strong limits on the existence of pure non-Abelian dark forces. On the other hand, if one or more of the dark glueballs are stable, we find that they can potentially make up the dark matter of the Universe.
One thousand and one bubbles

NASA Astrophysics Data System (ADS)

Ávila, Jesús; Ramírez, Pedro F.; Ruipérez, Alejandro

2018-01-01

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.
On spectroscopy for a whole Abelian model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600

Postulated on the whole meaning a whole abelian gauge symmetry is being introduced. Various physical areas as complexity, statistical mechanics, quantum mechanics are partially supporting this approach where the whole is at origin. However, the reductionist crisis given by quark confinement definitely sustains this insight. It says that fundamental parts can not be seen isolatedely. Consequently, there is an experimental situation where the parts should be substituted by something more. This makes us to look for writing the wholeness principle under gauge theory. For this, one reinterprets the gauge parameter where instead of compensating fields it is organizing a systemicmore » gauge symmetry. Now, it introduces a fields set {l_brace}A{sub {mu}I}{r_brace} rotating under a common gauge symmetry. Thus, given a fields collection {l_brace}A{sub {mu}I}{r_brace} as origin, the effort at this work is to investigate on its spectroscopy. Analyze for the abelian case the correspondent involved quanta. Understand that for a whole model diversity replaces elementarity. Derive the associated quantum numbers as spin, mass, charge, discrete symmetries in terms of such systemic symmetry. Observe how the particles diversity is manifested in terms of wholeness.« less
Experimental Investigation of the Electronic Properties of Twisted Bilayer Graphene by STM and STS

NASA Astrophysics Data System (ADS)

Yin, Longjing; Qiao, Jiabin; Wang, Wenxiao; Zuo, Weijie; He, Lin

The electronic properties of graphene multilayers depend sensitively on their stacking order. A twisted angle is treated as a unique degree of freedom to tune the electronic properties of graphene system. Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). We demonstrate that the interlayer coupling strength affects both the Van Hove singularities and the Fermi velocity of twisted bilayers dramatically. This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data. Moreover, we report the experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers by STM and STS. At a magic twisted angle, about 1.11°, a pronounced sharp peak is observed in the tunnelling spectra due to the action of the non-Abelian gauge fields. Because of the effective non-Abelian gauge fields, the rotation angle could transfer the charge carriers in the twisted bilayers from massless Dirac fermions into well localized electrons, or vice versa, efficiently. This provides a new route to tune the electronic properties of graphene systems, which will be essential in future graphene nanoelectronics.
Gluon and ghost correlation functions of 2-color QCD at finite density

NASA Astrophysics Data System (ADS)

Hajizadeh, Ouraman; Boz, Tamer; Maas, Axel; Skullerud, Jon-Ivar

2018-03-01

2-color QCD, i. e. QCD with the gauge group SU(2), is the simplest non-Abelian gauge theory without sign problem at finite quark density. Therefore its study on the lattice is a benchmark for other non-perturbative approaches at finite density. To provide such benchmarks we determine the minimal-Landau-gauge 2-point and 3-gluon correlation functions of the gauge sector and the running gauge coupling at finite density. We observe no significant effects, except for some low-momentum screening of the gluons at and above the supposed high-density phase transition.
Galaxy triplets in Sloan Digital Sky Survey Data Release 7 - II. A connection with compact groups?

NASA Astrophysics Data System (ADS)

Duplancic, Fernanda; O'Mill, Ana Laura; Lambas, Diego G.; Sodré, Laerte; Alonso, Sol

2013-08-01

We analyse a sample of 71 triplets of luminous galaxies derived from the work of O'Mill et al. We compare the properties of triplets and their members with those of control samples of compact groups, the 10 brightest members of rich clusters and galaxies in pairs. The triplets are restricted to have members with spectroscopic redshifts in the range 0.01 ≤ z ≤ 0.14 and absolute r-band luminosities brighter than Mr = -20.5. For these member galaxies, we analyse the stellar mass content, the star formation rates, the Dn(4000) parameter and (Mg - Mr) colour index. Since galaxies in triplets may finally merge in a single system, we analyse different global properties of these systems. We calculate the probability that the properties of galaxies in triplets are strongly correlated. We also study total star formation activity and global colours, and define the triplet compactness as a measure of the percentage of the system total area that is filled by the light of member galaxies. We concentrate in the comparison of our results with those of compact groups to assess how the triplets are a natural extension of these compact systems. Our analysis suggests that triplet galaxy members behave similarly to compact group members and galaxies in rich clusters. We also find that systems comprising three blue, star-forming, young stellar population galaxies (blue triplets) are most probably real systems and not a chance configuration of interloping galaxies. The same holds for triplets composed of three red, non-star-forming galaxies, showing the correlation of galaxy properties in these systems. From the analysis of the triplet as a whole, we conclude that, at a given total stellar mass content, triplets show a total star formation activity and global colours similar to compact groups. However, blue triplets show a high total star formation activity with a lower stellar mass content. From an analysis of the compactness parameter of the systems we find that light is even more concentrated in triplets than in compact groups. We propose that triplets composed of three luminous galaxies, should not be considered as an analogous of galaxy pairs with a third extra member, but rather they are a natural extension of compact groups.
Degradation of trans-polyisoprene after root filling with thermoplasticized techniques.

PubMed

Maniglia-Ferreira, C; Bönecker, G; Silva, J B A; de Paula, R C M; Feitosa, J P A; Souza-Filho, F J

2008-04-01

To evaluate ex vivo degradation of gutta-percha following six thermoplastic obturation techniques. Ninety human-extracted mandibular premolars were selected and divided randomly into nine groups for filling. Group 1: thermomechanical compaction for 3 s with Konne gutta-percha points (Konne Ind. e Com. de Mat. Odontol., Belo Horizonte, MG, Brazil); Group 2: thermomechanical compaction for 3 s with Dentsply TP gutta-percha points (Dentsply Indústria e Comércio Ltda, Petrópolis, R.J. Brazil); Group 3: thermomechanical compaction for 10 s with Konne; Group 4: thermomechanical compaction for 10 s with Dentsply TP; Group 5: warm vertical condensation using System B (EIE/Analytic, Richmond, WA, USA) with Konne; Group 6: warm vertical condensation using System B with Dentsply TP; Group 7: vertical condensation with Konne; Group 8: vertical condensation with Dentsply TP; Group 9: Microseal cone (Analytic Endodontics, Glendora, CA, USA). A further four groups were assessed without using teeth, Group 10: Microseal microflow (Analytic Endodontics); Group 11: Obtura (Obtura Corporation, Penton, MO, USA); Group 12: Obtura flow (Obtura Corporation); Group 13: Thermafil (Dentsply Maillefer, Tulsa, OK, USA). The filling material was removed from the root canal and trans-1,4-polyisoprene isolated by solubilization of the root filling remnants in chloroform followed by filtration and centrifugation. By gel permeation chromatography and infrared spectroscopy, the occurrence and degree of degradation were assessed. The results were analysed statistically using the Kruskal-Wallis test. With differential scanning calorimetry, the thermal behaviour of the gutta-percha was determined. A significant decrease in polymer molar mass and the production of carboxyl and hydroxyl groups in the polymer were observed with thermomechanical compaction used for 10 s and vertical condensation filling techniques (P = 0.0001 and P = 0.0005, respectively). Other techniques caused no polymer degradation. Polyisoprene degrades with high temperature. Thermomechanical compaction for 10 s and vertical condensation were associated with the greatest degradative process.
Sealing ability of lateral compaction and tapered single cone gutta-percha techniques in root canals prepared with stainless steel and rotary nickel titanium instruments.

PubMed

Koçak, Mustafa M; Darendeliler-Yaman, Sis

2012-07-01

The aim of this study was to evaluate the sealing ability of lateral compaction and tapered single cone gutta-percha techniques in root canals prepared with stainless steel and rotary nickel titanium root canal instruments by fluid filtration method. The root canals were prepared with stainless steel (SS) and nickel titanium (NiTi) instruments. The canals prepared with SS were obturated with lateral compaction technique using .02 tapered cones and the canals prepared with NiTi instruments were obturated with lateral compaction technique using .02 tapered cones or 06 tapered single cones. The amount of leakage was evaluated by fluid filtration model. The results were statistically analyzed with one-way ANOVA. The group prepared with NiTi instruments and filled with lateral compaction technique showed significantly less coronal leakage than the group prepared with SS instruments and filled with lateral compaction technique (p<0.05). There was no statistically difference between apical leakages of groups (p>0.05). Obturation with lateral compaction of gutta-percha provides a superior coronal seal whilst canal instrumentation with engine-driven NiTi files reduces the extent of microleakage in root canals when compared with stainless steel hand instruments. Tapered single cone technique was comparable with lateral compaction technique because of easier application. Key words:Apical leakage, coronal leakage, lateral compaction technique, single cone technique.
A Search for X-ray Emission in Isolated Compact Triplets

NASA Technical Reports Server (NTRS)

Brown, Beth A.; Williams, Barbara

2006-01-01

We describe preliminary results of an exploratory search for diffuse X-ray emission in a sample of the poorest galaxy groups, i.e., isolated compact triplets of galaxies. These systems represent the simplest forms of galaxy clustering while manifesting all the complexities inherent in other groups. We have selected 20 compact triplets for this initial study. The component galaxies are expected to interact with each other and with the group's intergalactic medium, if present, in complex ways that trigger high-energy processes.
Non-Abelian fermionization and fractional quantum Hall transitions

NASA Astrophysics Data System (ADS)

Hui, Aaron; Mulligan, Michael; Kim, Eun-Ah

2018-02-01

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent ν ≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi et al., Rev. Mod. Phys. 69, 315 (1997), 10.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U (Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf≫Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf≫Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993), 10.1103/PhysRevLett.70.1501; Chen et al., Phys. Rev. B 48, 13749 (1993), 10.1103/PhysRevB.48.13749].
Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

2005-03-01

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace-type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding 1-loop divergences and 1-loop effective action actually exists. The present paper shows that, on the Euclidean 4-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is 'confined' to the remaining fourth sector. The integral representation of the resulting ζ-function asymptotics on the Euclidean 4-ball is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.

The 'sleeping beauty' galaxy NGC 4826: an almost textbook example of the Abelian Higgs vorto-source (-sink)

NASA Astrophysics Data System (ADS)

Saniga, Metod

1995-03-01

It is demonstrated that the kinematic 'peculiarity' of the early Sab galaxy NGC 4826 can easily be understood in terms of the Abelian Higgs (AH) model of spiral galaxies. A cylindrically symmetric AH vorto-source (-sink) with a disk-to-bulge ratio Omega greater than 1 is discussed and the distributions of the diagonal components of the corresponding stress-energy tensor Tmu,nu are presented. It is argued that the sign-changing component Tphiphi could account for the existence of two counter-rotating gas disks while negative values of Trr imply inward gas motions as observed in the outer and transition regions of the galaxy.
Dirac-Born-Infeld actions and tachyon monopoles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calo, Vincenzo; Tallarita, Gianni; Thomas, Steven

2010-04-15

We investigate magnetic monopole solutions of the non-Abelian Dirac-Born-Infeld (DBI) action describing two coincident non-BPS D9-branes in flat space. Just as in the case of kink and vortex solitonic tachyon solutions of the full DBI non-BPS actions, as previously analyzed by Sen, these monopole configurations are singular in the first instance and require regularization. We discuss a suitable non-Abelian ansatz that describes a pointlike magnetic monopole and show it solves the equations of motion to leading order in the regularization parameter. Fluctuations are studied and shown to describe a codimension three BPS D6-brane, and a formula is derived for itsmore » tension.« less
The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.
Topological degeneracy of non-Abelian states for dummies

NASA Astrophysics Data System (ADS)

Oshikawa, Masaki; Kim, Yong Baek; Shtengel, Kirill; Nayak, Chetan; Tewari, Sumanta

2007-06-01

We present a physical construction of degenerate groundstates of the Moore-Read Pfaffian states, which exhibits non-Abelian statistics, on general Riemann surface with genus g. The construction is given by a generalization of the recent argument [M.O., T. Senthil, Phys. Rev. Lett. 96 (2006) 060601] which relates fractionalization and topological order. The nontrivial groundstate degeneracy obtained by Read and Green [Phys. Rev. B 61 (2000) 10267] based on differential geometry is reproduced exactly. Some restrictions on the statistics, due to the fractional charge of the quasiparticle are also discussed. Furthermore, the groundstate degeneracy of the p + i p superconductor in two dimensions, which is closely related to the Pfaffian states, is discussed with a similar construction.
A string realisation of Ω-deformed Abelian N =2* theory

NASA Astrophysics Data System (ADS)

Angelantonj, Carlo; Antoniadis, Ignatios; Samsonyan, Marine

2017-10-01

The N =2* supersymmetric gauge theory is a massive deformation of N = 4, in which the adjoint hypermultiplet gets a mass. We present a D-brane realisation of the (non-)Abelian N =2* theory, and compute suitable topological amplitudes, which are expressed as a double series expansion. The coefficients determine couplings of higher-dimensional operators in the effective supergravity action that involve powers of the anti-self-dual N = 2 chiral Weyl superfield and of self-dual gauge field strengths superpartners of the D5-brane coupling modulus. In the field theory limit, the result reproduces the Nekrasov partition function in the two-parameter Ω-background, in agreement with a recent proposal.
Chiral Magnetic Effect and Anomalous Transport from Real-Time Lattice Simulations

DOE PAGES

Müller, Niklas; Schlichting, Sören; Sharma, Sayantan

2016-09-30

Here, we present a first-principles study of anomaly induced transport phenomena by performing real-time lattice simulations with dynamical fermions coupled simultaneously to non-Abelian S U ( N c ) and Abelian U ( 1 ) gauge fields. By investigating the behavior of vector and axial currents during a sphaleron transition in the presence of an external magnetic field, we demonstrate how the interplay of the chiral magnetic and chiral separation effect leads to the formation of a propagating wave. Furthermore, we analyze the dependence of the magnitude of the induced vector current and the propagation of the wave on themore » amount of explicit chiral symmetry breaking due to finite quark masses.« less
Enhanced gauge symmetry in type II and F-theory compactifications: Dynkin diagrams from polyhedra

NASA Astrophysics Data System (ADS)

Perevalov, Eugene; Skarke, Harald

1997-02-01

We explain the observation by Candelas and Font that the Dynkin diagrams of non-abelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron Δ ∗ that provides the toric description of the Calabi-Yau manifold used for compactification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also explain how even the occurrence of monodromy and non-simply laced groups in the latter case is visible in the toric picture. These methods also work in the fourfold case.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms

PubMed Central

Huo, Ming-Xia; Nie, Wei; Hutchinson, David A. W.; Kwek, Leong Chuan

2014-01-01

Cold neutral atoms provide a versatile and controllable platform for emulating various quantum systems. Despite efforts to develop artificial gauge fields in these systems, realizing a unique ideal-solenoid-shaped magnetic field within the quantum domain in any real-world physical system remains elusive. Here we propose a scheme to generate a “hairline” solenoid with an extremely small size around 1 micrometer which is smaller than the typical coherence length in cold atoms. Correspondingly, interference effects will play a role in transport. Despite the small size, the magnetic flux imposed on the atoms is very large thanks to the very strong field generated inside the solenoid. By arranging different sets of Laguerre-Gauss (LG) lasers, the generation of Abelian and non-Abelian SU(2) lattice gauge fields is proposed for neutral atoms in ring- and square-shaped optical lattices. As an application, interference patterns of the magnetic type-I Aharonov-Bohm (AB) effect are obtained by evolving atoms along a circle over several tens of lattice cells. During the evolution, the quantum coherence is maintained and the atoms are exposed to a large magnetic flux. The scheme requires only standard optical access, and is robust to weak particle interactions. PMID:25103877
Anisotropic Bispectrum of Curvature Perturbations from Primordial Non-Abelian Vector Fields

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Dimastrogiovanni, Emanuela; Matarrese, Sabino; Riotto, Antonio

2009-10-01

We consider a primordial SU(2) vector multiplet during inflation in models where quantum fluctuations of vector fields are involved in producing the curvature perturbation. Recently, a lot of attention has been paid to models populated by vector fields, given the interesting possibility of generating some level of statistical anisotropy in the cosmological perturbations. The scenario we propose is strongly motivated by the fact that, for non-Abelian gauge fields, self-interactions are responsible for generating extra terms in the cosmological correlation functions, which are naturally absent in the Abelian case. We compute these extra contributions to the bispectrum of the curvature perturbation, using the δN formula and the Schwinger-Keldysh formalism. The primordial violation of rotational invariance (due to the introduction of the SU(2) gauge multiplet) leaves its imprint on the correlation functions introducing, as expected, some degree of statistical anisotropy in our results. We calculate the non-Gaussianity parameter fNL, proving that the new contributions derived from gauge bosons self-interactions can be important, and in some cases the dominat ones. We study the shape of the bispectrum and we find that it turns out to peak in the local configuration, with an amplitude that is modulated by the preferred directions that break statistical isotropy.
On discrete symmetries for a whole Abelian model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chauca, J.; Doria, R.; Aprendanet, Petropolis, 25600

Considering the whole concept applied to gauge theory a nonlinear abelian model is derived. A next step is to understand on the model properties. At this work, it will be devoted to discrete symmetries. For this, we will work based in two fields reference systems. This whole gauge symmetry allows to be analyzed through different sets which are the constructor basis {l_brace}D{sub {mu}},X{sup i}{sub {mu}}{r_brace} and the physical basis {l_brace}G{sub {mu}I}{r_brace}. Taking as fields reference system the diagonalized spin-1 sector, P, C, T and PCT symmetries are analyzed. They show that under this systemic model there are conservation laws drivenmore » for the parts and for the whole. It develops the meaning of whole-parity, field-parity and so on. However it is the whole symmetry that rules. This means that usually forbidden particles as pseudovector photons can be introduced through such whole abelian system. As result, one notices that the fields whole {l_brace}G{sub {mu}I}{r_brace} manifest a quanta diversity. It involves particles with different spins, masses and discrete quantum numbers under a same gauge symmetry. It says that without violating PCT symmetry different possibilities on discrete symmetries can be accommodated.« less
Directed Abelian algebras and their application to stochastic models.

PubMed

Alcaraz, F C; Rittenberg, V

2008-10-01

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .
Environmental influences on galaxy evolution

NASA Technical Reports Server (NTRS)

Zepf, Stephen E.; Whitmore, Bradley C.

1993-01-01

We investigate the role of mergers and interactions in the evolution of galaxies by studying galaxies in compact groups. Compact groups of galaxies have high spatial densities and low velocity dispersions making these regions ideal laboratories in which to study the effect of interactions and mergers. Based on a detailed spectroscopic and multi-color imaging study, we find that both the isophotal shapes and the stellar kinematics indicate that many of the elliptical galaxies in compact groups have been affected by tidal interactions. At the same time, however, we find that only a few elliptical galaxies in compact groups have evidence for the young stellar populations that would be expected if they are the result of recent merger of two spiral galaxies. Therefore, we conclude that tidal interactions affect galaxy properties at the current epoch, but the bulk of basic galaxy formation and transformation must have occurred at much higher redshift.
Rigid Calabi-Yau threefolds, Picard Eisenstein series and instantons

NASA Astrophysics Data System (ADS)

Bao, L.; Kleinschmidt, A.; Nilsson, B. E. W.; Persson, D.; Pioline, B.

2013-12-01

Type IIA string theory compactified on a rigid Calabi-Yau threefold gives rise to a classical moduli space that carries an isometric action of U(2, 1). Various quantum corrections break this continuous isometry to a discrete subgroup. Focussing on the case where the intermediate Jacobian of the Calabi-Yau admits complex multiplication by the ring of quadratic imaginary integers d, we argue that the remaining quantum duality group is an arithmetic Picard modular group PU(2, 1; d). Based on this proposal we construct an Eisenstein series invariant under this duality group and study its non-Abelian Fourier expansion. This allows the prediction of non-perturbative effects, notably the contribution of D2- and NS5-brane instantons. The present work extends our previous analysis in 0909.4299 which was restricted to the special case of the Gaussian integers 1 = Bbb Z[i].
Quantum spaces, central extensions of Lie groups and related quantum field theories

NASA Astrophysics Data System (ADS)

Poulain, Timothé; Wallet, Jean-Christophe

2018-02-01

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.
Spin waves, vortices, fermions, and duality in the Ising and Baxter models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ogilvie, M.C.

1981-10-15

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex+spin-wave decomposition, that the Z/sub p/-Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves conspire to produce a free, massive Majorana field theory in the continuum limit. The continuum limit of the Baxter model is also studied, and the recent results of Kadanoff and Brown are rederived and extended.
Counting spinning dyons in maximal supergravity: the Hodge-elliptic genus for tori

NASA Astrophysics Data System (ADS)

Benjamin, Nathan; Kachru, Shamit; Tripathy, Arnav

2017-11-01

We consider M-theory compactified on T^4 × T^2 and describe the count of spinning 1/8-BPS states. This builds on the work of Maldacena-Moore-Strominger in the physics literature. It simultaneously provides a refinement of the recent mathematical work of Bryan-Oberdieck-Pandharipande-Yin and Oberdieck-Shen, which studied (non-motivic) reduced Donaldson-Thomas invariants of abelian surfaces and threefolds. As in previous work on K3 × T^2 compactification, we track angular momenta under both the SU(2)_L and SU(2)_R factors in the 5d little group, providing predictions for the relevant motivic curve counts.
Separation of variables for the Dirac equation in an extended class of Lorentzian metrics with local rotational symmetry

NASA Astrophysics Data System (ADS)

Iyer, B. R.; Kamran, N.

1991-09-01

The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.
Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

NASA Astrophysics Data System (ADS)

Gracey, J. A.; Simms, R. M.

2018-04-01

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter ω , which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.
Non-Abelian vortex lattices

NASA Astrophysics Data System (ADS)

Tallarita, Gianni; Peterson, Adam

2018-04-01

We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.
A simple model for the evolution of a non-Abelian cosmic string network

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cella, G.; Pieroni, M., E-mail: giancarlo.cella@pi.infn.it, E-mail: mauro.pieroni@apc.univ-paris7.fr

2016-06-01

In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we variate the number of generators for the topological defects. A simple model which allows for cosmic strings is presented and its lattice discretization is discussed. The evolution of the generated cosmic string networks is then studied for different values for the number of generators for the topological defects. Scaling solution appears to be approached in most cases and we present an argumentmore » to justify the lack of scaling for the residual cases.« less

Andreev bound states in a semiconducting nanowire Josephson junction, Part II: Quantum jumps and Fermion parity switching

NASA Astrophysics Data System (ADS)

Hays, M.; de Lange, G.; Serniak, K.; van Woerkom, D. J.; Väyrynen, J. I.; van Heck, B.; Vool, U.; Krogstrup, P.; Nygård, J.; Frunzio, L.; Geresdi, A.; Glazman, L. I.; Devoret, M. H.

Proximitized semiconducting nanowires subject to magnetic field should display topological superconductivity and support Majorana zero modes which have non-Abelian braiding statistics. The conventional Andreev levels formed in such wires in the absence of field are a precursor to these exotic zero modes. The fermion-parity switching time of Andreev levels sets a lower bound on the bandwidth required for experiments aimed at harnessing non-Abelian braiding statistics. We demonstrate the observation of quantum jumps between even and odd-parity states of an individual Andreev bound state in a non-topological junction, providing a direct measurement of the state populations and the parity lifetime. Work supported by: ARO, ONR, AFOSR, EU Marie Curie and YINQE.
Faint Dwarf Galaxies in Hickson Compact Group 90

NASA Astrophysics Data System (ADS)

Ordenes-Briceño, Y.; Taylor, M. A.; Puzia, T. H.; Muñoz, R. P.

2017-07-01

We report the discovery of a very diverse set of five low-surface brightness (LSB) dwarf galaxy candidates in Hickson Compact Group 90 (HCG 90) detected in deep U- and I-band images obtained with VLT/VIMOS. These are the first LSB dwarf galaxy candidates found in a compact group of galaxies, which share properties with dwarf galaxies found throughout the Local Volume and in nearby galaxy clusters such as Fornax. Among them, we find a pair of candidates with ˜2 kpc projected separation and a nucleated dwarf candidate, with nucleus size of reff≅46-63 pc.
On orthogonal projectors induced by compact groups and Haar measures

NASA Astrophysics Data System (ADS)

Niezgoda, Marek

2008-02-01

We study the difference of two orthogonal projectors induced by compact groups of linear operators acting on a vector space. An upper bound for the difference is derived using the Haar measures of the groups. A particular attention is paid to finite groups. Some applications are given for complex matrices and unitarily invariant norms. Majorization inequalities of Fan and Hoffmann and of Causey are rediscovered.
Extension of transformation groups of compact solvmanifolds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milovanov, M V

2015-04-30

We indicate a way to extend connected simply connected soluble Lie groups acting transitively and locally effectively on a given compact solvmanifold. In 1973, Auslander posed the problem of describing all groups of this kind. The results obtained here lead to the conclusion that it is unlikely that this problem has an exhaustive solution. Bibliography: 10 titles.
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2017-03-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson’s RG for lattice gauge theories. Although Migdal’s RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN’s results gave a theoretical formulation foundation and justification for BKT’s sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory.
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition

NASA Astrophysics Data System (ADS)

José, Jorge V.

2013-06-01

In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested successfully against experimental results on superfluid helium films. The success of the BKT theory also gave one of the first quantitative proofs of the validity of the RG theory...
Antimicrobial photodynamic inactivation of Staphylococcus aureus biofilms in bone specimens using methylene blue, toluidine blue ortho and malachite green: An in vitro study.

PubMed

Rosa, Luciano Pereira; da Silva, Francine Cristina; Nader, Sumaia Alves; Meira, Giselle Andrade; Viana, Magda Souza

2015-05-01

To evaluate the in vitro effectiveness of APDI with a 660 nm laser combined with methylene blue (MB), toluidine blue ortho (TBO) and malachite green (MG) dyes to inactivate Staphylococcus aureus (ATCC 25923) biofilms in compact and cancellous bone specimens. Eighty specimens of compact and 80 of cancellous bone were contaminated with a standard suspension of the microorganism and incubated for 14 days at 37°C to form biofilms. After this period, the specimens were divided into groups (n=10) according to established treatment: PS-L- (control - no treatment); PSmb+L-, PStbo+L-, PSmg+L- (only MB, TBO or MG for 5 min in the dark); PS-L+ (only laser irradiation for 180 s); and APDImb, APDItbo and APDImg (APDI with MB, TBO or MG for 180 s). The findings were statistically analyzed by ANOVA at 5% significance levels. All experimental treatments showed significant reduction of log CFU/mL S. aureus biofilms when compared with the control group for compact and cancellous bones specimens; the APDI group's treatment was more effective. The APDI carried out for the compact specimens showed better results when compared with cancellous specimens at all times of application. For the group of compact bone, APDImg showed greater reductions in CFU/mL (4.46 log 10). In the group of cancellous bone, the greatest reductions were found in the APDImb group (3.06 log 10). APDI with methylene blue, toluidine blue ortho and malachite green dyes and a 660 nm laser proved to be effective in the inactivation of S. aureus biofilms formed in compact and cancellous bone. Copyright © 2015 Elsevier Ltd. All rights reserved.
Preparation of the Femoral Bone Cavity for Cementless Stems: Broaching vs Compaction. A Five-Year Randomized Radiostereometric Analysis and Dual Energy X-Ray Absorption Study.

PubMed

Hjorth, Mette H; Kold, Søren; Søballe, Kjeld; Langdahl, Bente L; Nielsen, Poul T; Christensen, Poul H; Stilling, Maiken

2017-06-01

Short-term experimental and animal studies have confirmed superior fixation of cementless implants inserted with compaction compared to broaching of the cancellous bone. Forty-four hips in 42 patients (19 men) were randomly operated using cementless hydroxyapatite-coated Bi-Metric stems. Patients were followed with radiostereometric analysis at baseline, 6 and 12 weeks, 1, 2, and 5 years, and measurements of periprosthetic bone mineral density at baseline, 1, 2, and 5 years. Complications during the study period and clinical outcome measures of Harris Hip Score were recorded at mean 7 years (5-8.8) after surgery. Absolute migrations of medio/lateral translations between the broaching group and the compaction group of mean 0.14 mm (standard deviation [SD] 0.10) vs mean 0.30 mm (SD 0.27) (P = .01) at 1 year, and of mean 0.13 mm (SD 0.10) vs 0.34 mm (0.31) (P = .01) at 5 years were different. Absolute valgus/varus rotations of mean 0.12° (SD 0.13°) in the broaching group were less than mean 0.35° (0.45°) in the compaction group (P < .01) at 1 year, but at 5 years no difference was observed (P = .19). Subsidence and retroversion were similar between groups at all follow-ups (P > .13). The compaction group had significantly less bone loss than the broaching group in Gruen zone 3 (distal-lateral to the stem) at 1 and 5 years. No further differences in bone mineral density changes were found between groups up to 5 years after surgery. Complications throughout the period and clinical outcome measures of Harris Hip Score were similar at 7 years (5-8.8) after surgery. We found increased migration when preparing the bone with compaction compared with broaching in cementless femoral stems. Copyright © 2017 Elsevier Inc. All rights reserved.
Moduli space potentials for heterotic non-Abelian flux tubes: Weak deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shifman, M.; Yung, A.; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300

2010-09-15

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N{sub f} flavors of massive quarks deformed by the mass term {mu} for the adjoint matter, W={mu}A{sup 2}, assuming that N{<=}N{sub f}<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small {mu}, so that the Z{sub N} strings preserve, in a sense, their Bogomol'nyi-Prasad-Sommerfield nature. The (s)quark massesmore » are assumed to be nondegenerate. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N{sub f}-1) model on the string world sheet. The bulk {mu} deformation makes this theory N=(0,2) supersymmetric heterotic weighted CP(N{sub f}-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.« less
VizieR Online Data Catalog: X-ray sources in Hickson Compact Groups (Tzanavaris+, 2014)

NASA Astrophysics Data System (ADS)

Tzanavaris, P.; Gallagher, S. C.; Hornschemeier, A. E.; Fedotov, K.; Eracleous, M.; Brandt, W. N.; Desjardins, T. D.; Charlton, J. C.; Gronwall, C.

2014-06-01

By virtue of their selection criteria, Hickson Compact Groups (HCGs) constitute a distinct class among small galaxy agglomerations. The Hickson catalog (Hickson et al. 1992, Cat. VII/213) comprises 92 spectroscopically confirmed nearby compact groups with three or more members with accordant redshifts (i.e., within 1000km/s of the group mean). In this paper we present nine of these groups, for which both archival Chandra X-ray and Swift UVOT ultraviolet data are available. An observation log for the Chandra data is presented in Table 1. An observation log for the Swift UVOT data is presented in Tzanavaris et al. (2010ApJ...716..556T). In addition, note that in the present work we have included UVOT data for HCGs 90 and 92. (3 data files).
Confining and repulsive potentials from effective non-Abelian gauge fields in graphene bilayers

NASA Astrophysics Data System (ADS)

González, J.

2016-10-01

We investigate the effect of shear and strain in graphene bilayers, under conditions where the distortion of the lattice gives rise to a smooth one-dimensional modulation in the stacking sequence of the bilayer. We show that strain and shear produce characteristic Moiré patterns which can have the same visual appearance on a large scale, but representing graphene bilayers with quite different electronic properties. The different features in the low-energy electronic bands can be ascribed to the effect of a fictitious non-Abelian gauge field mimicking the smooth modulation of the stacking order. Strained and sheared bilayers show a complementary behavior, which can be understood from the fact that the non-Abelian gauge field acts as a repulsive interaction in the former, expelling the electron density away from the stacking domain walls, while behaving as a confining interaction leading to localization of the electronic states in the sheared bilayers. In this latter case, the presence of the effective gauge field explains the development of almost flat low-energy bands, resembling the form of the zeroth Landau level characteristic of a Dirac fermion field. The estimate of the gauge field strength in those systems gives a magnitude of the order of several tens of tesla, implying a robust phenomenology that should be susceptible of being observed in suitably distorted bilayer samples.
Intersecting solitons, amoeba, and tropical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujimori, Toshiaki; Nitta, Muneto; Ohta, Kazutoshi

2008-11-15

We study the generic intersection (or web) of vortices with instantons inside, which is a 1/4 Bogomol'nyi-Prasad-Sommerfield state in the Higgs phase of five-dimensional N=1 supersymmetric U(N{sub C}) gauge theory on R{sub t}x(C*){sup 2}{approx_equal}R{sup 2,1}xT{sup 2} with N{sub F}=N{sub C} Higgs scalars in the fundamental representation. In the case of the Abelian-Higgs model (N{sub F}=N{sub C}=1), the intersecting vortex sheets can be beautifully understood in a mathematical framework of amoeba and tropical geometry, and we propose a dictionary relating solitons and gauge theory to amoeba and tropical geometry. A projective shape of vortex sheets is described by the amoeba. Vortexmore » charge density is uniformly distributed among vortex sheets, and negative contribution to instanton charge density is understood as the complex Monge-Ampere measure with respect to a plurisubharmonic function on (C*){sup 2}. The Wilson loops in T{sup 2} are related with derivatives of the Ronkin function. The general form of the Kaehler potential and the asymptotic metric of the moduli space of a vortex loop are obtained as a by-product. Our discussion works generally in non-Abelian gauge theories, which suggests a non-Abelian generalization of the amoeba and tropical geometry.« less
VLA neutral hydrogen imaging of compact groups

NASA Technical Reports Server (NTRS)

Williams, B. A.; Mcmahon, P. M.; Vangorkom, J. H.

1990-01-01

Images of the neutral hydrogen (H I) in the direction of the compact groups of galaxies, HCG 31, HCG 44, and HCG 79 are presented. The authors find in HCG 31 and HCG 79, emission contained within a cloud much larger than the galaxies as well as the entire group. The H I emission associated with HCG 44 is located within the individual galaxies but shows definite signs of tidal interactions. The authors imaged the distribution and kinematics of neutral hydrogen at the two extremes of group sizes represented in Hickson's sample. HCG 44 is at the upper limit while HCG 18, HCG 31, and HCG 79 are at the lower end. Although the number of groups that have been imaged is still very small, there may be a pattern emerging which describes the H I morphology of compact groups. The true nature of compact groups has been the subject of considerable debate and controversy. The most recent observational and theoretical evidence strongly suggests that compact groups are physically dense, dynamical systems that are in the process of merging into a single object (Williams and Rood 1987, Hickson and Rood 1988, Barnes 1989). The neutral hydrogen deficiency observed by Williams and Rood (1987) is consistent with a model in which frequent galactic collisions and interactions have heated some of the gas during the short lifetime of the group. The H I disks which are normally more extended than the luminous ones are expected to be more sensitive to collisions and to trace the galaxy's response to recent interactions. Very Large Array observations can provide in most cases the spatial resolution needed to confirm the dynamical interactions in these systems.
Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.
Compact Eucapnic Voluntary Hyperpnoea Apparatus for Exercise-Induced Respiratory Disease Detection

PubMed Central

Wang, Lulu; Al-Jumaily, Ahmed

2017-01-01

Eucapnic voluntary hyperpnoea (EVH) challenge provides objective criteria for exercise-induced asthma (EIA) or exercise-induced bronchoconstriction (EIB), and it was recommended to justify the use of inhaled β2-agonists by athletes for the Olympics. This paper presents the development of a compact and easy-to-use EVH apparatus for assessing EIB in human subjects. The compact apparatus has been validated on human subjects and the results have been compared to the conventional EVH system. Twenty-two swimmers, including eleven healthy subjects and eleven subjects who had been physician-diagnosed with asthma, were recruited from sport and recreation centers throughout Auckland, New Zealand. Each subject performed two EVH challenge tests using the proposed breathing apparatus and the conventional Phillips EVH apparatus on separate days, respectively. Forced expiratory volume in one second (FEV1) was measured before and after the challenges. A reduction in FEV1 of 10% or more was considered positive. Of the eleven subjects who were previously diagnosed with asthma, EIB was present in all subjects (100%) in the compact EVH group, while it was presented in ten subjects (90.91%) in the conventional EVH challenge group. Of the eleven healthy subjects, EIB was present in one subject (4.55%) in the compact EVH group, while it was not present in the conventional EVH group. Experimental results showed that the compact EVH system has potential to become an alternative tool for EIB detection. PMID:28509868
Kibble-Zurek scaling and string-net coarsening in topologically ordered systems.

PubMed

Chandran, Anushya; Burnell, F J; Khemani, Vedika; Sondhi, S L

2013-10-09

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now without the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the Abelian Z2 topologically ordered phase of the toric code/Z2 gauge theory, and the non-Abelian SU(2)k ordered phases of the relevant Levin-Wen models.
Abelianization and sequential confinement in 2 + 1 dimensions

NASA Astrophysics Data System (ADS)

Benvenuti, Sergio; Giacomelli, Simone

2017-10-01

We consider the lagrangian description of Argyres-Douglas theories of type A 2 N -1, which is a SU( N) gauge theory with an adjoint and one fundamental flavor. An appropriate reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD "abelianizes": in the infrared it is equivalent to a N=4 linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to "sequentially confine" quivers tails with balanced nodes, we show that the mirror RG flow lands on N=4 SQED with N flavors. These results make the supersymmetry enhancement explicit and provide a physical derivation of previous proposals for the three dimensional mirror of AD theories.
Lagrangians for generalized Argyres-Douglas theories

NASA Astrophysics Data System (ADS)

Benvenuti, Sergio; Giacomelli, Simone

2017-10-01

We continue the study of Lagrangian descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.
Formation of helical domain walls in the fractional quantum Hall regime as a step toward realization of high-order non-Abelian excitations

NASA Astrophysics Data System (ADS)

Wu, Tailung; Wan, Zhong; Kazakov, Aleksandr; Wang, Ying; Simion, George; Liang, Jingcheng; West, Kenneth W.; Baldwin, Kirk; Pfeiffer, Loren N.; Lyanda-Geller, Yuli; Rokhinson, Leonid P.

2018-06-01

We propose an experimentally feasible platform to realize parafermions (high-order non-Abelian excitations) based on spin transitions in the fractional quantum Hall effect regime. As a proof of concept we demonstrate a local control of the spin transition at a filling factor 2/3 and formation of a conducting fractional helical domain wall (fhDW) along a gate boundary. Coupled to an s -wave superconductor these fhDWs are expected to support parafermionic excitations. We present exact diagonalization numerical studies of fhDWs and show that they indeed possess electronic and magnetic structures needed for the formation of parafermions. A reconfigurable network of fhDWs will allow manipulation and braiding of parafermionic excitations in multigate devices.
Quantum corrections to non-Abelian SUSY theories on orbifolds

NASA Astrophysics Data System (ADS)

Groot Nibbelink, Stefan; Hillenbach, Mark

2006-07-01

We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S/Z and T/Z, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non- Z fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.

More on quantum groups from the quantization point of view

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1994-12-01

Star products on the classical double group of a simple Lie group and on corresponding symplectic groupoids are given so that the quantum double and the “quantized tangent bundle” are obtained in the deformation description. “Complex” quantum groups and bicovariant quantum Lie algebras are discussed from this point of view. Further we discuss the quantization of the Poisson structure on the symmetric algebra S(g) leading to the quantized enveloping algebra U h (g) as an example of biquantization in the sense of Turaev. Description of U h (g) in terms of the generators of the bicovariant differential calculus on F(G q ) is very convenient for this purpose. Finaly we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducble representation in the compact case.
Comparative evaluation of fracture resistance of root canals obturated with four different obturating systems

PubMed Central

Punjabi, Mansi; Dewan, Ruchika Gupta; Kochhar, Rohit

2017-01-01

Aim and Objectives: The aim of this study is to evaluate and compare the fracture resistance of root canals obturated with four different obturating systems in endodontically treated teeth. Materials and Methods: One hundred and twenty single-rooted teeth were selected and decoronated at cementoenamel junction. Instrumentation of teeth (except control group) was done with Mtwo rotary files up to size 25/0.06 using a step-back technique. All teeth were divided into four experimental groups (n = 25) and two control groups (n = 10). In Group I (negative control), teeth were neither instrumented nor obturated, in Group II (positive control), instrumentation was done, but no obturation was performed, in Group III, obturation was done with cold lateral compaction technique, in Group IV, obturation was done with cold free-flow compaction technique, in Group V, obturation was done with warm vertical compaction technique, and in Group VI, obturation was done with injection-molded thermoplasticized technique. All prepared teeth were embedded in an acrylic resin block, and their fracture strength was measured using Universal Testing Machine. Statistical data were analyzed using one-way analysis of variance and Tukey's honestly significant difference test. Results: Negative control Group I showed highest fracture resistance and positive control Group II had lowest fracture resistance. Among experimental groups, cold free-flow compaction technique with GuttaFlow2 (Group IV) showed higher fracture resistance as compared to the Group III, Group V, and Group VI. Conclusion: GuttaFlow2 has the potential to strengthen the endodontically treated roots to a level that is similar to that of intact teeth. PMID:29430099
Comparative evaluation of fracture resistance of root canals obturated with four different obturating systems.

PubMed

Punjabi, Mansi; Dewan, Ruchika Gupta; Kochhar, Rohit

2017-01-01

The aim of this study is to evaluate and compare the fracture resistance of root canals obturated with four different obturating systems in endodontically treated teeth. One hundred and twenty single-rooted teeth were selected and decoronated at cementoenamel junction. Instrumentation of teeth (except control group) was done with Mtwo rotary files up to size 25/0.06 using a step-back technique. All teeth were divided into four experimental groups ( n = 25) and two control groups ( n = 10). In Group I (negative control), teeth were neither instrumented nor obturated, in Group II (positive control), instrumentation was done, but no obturation was performed, in Group III, obturation was done with cold lateral compaction technique, in Group IV, obturation was done with cold free-flow compaction technique, in Group V, obturation was done with warm vertical compaction technique, and in Group VI, obturation was done with injection-molded thermoplasticized technique. All prepared teeth were embedded in an acrylic resin block, and their fracture strength was measured using Universal Testing Machine. Statistical data were analyzed using one-way analysis of variance and Tukey's honestly significant difference test. Negative control Group I showed highest fracture resistance and positive control Group II had lowest fracture resistance. Among experimental groups, cold free-flow compaction technique with GuttaFlow2 (Group IV) showed higher fracture resistance as compared to the Group III, Group V, and Group VI. GuttaFlow2 has the potential to strengthen the endodontically treated roots to a level that is similar to that of intact teeth.
Permutation on hybrid natural inflation

NASA Astrophysics Data System (ADS)

Carone, Christopher D.; Erlich, Joshua; Ramos, Raymundo; Sher, Marc

2014-09-01

We analyze a model of hybrid natural inflation based on the smallest non-Abelian discrete group S3. Leading invariant terms in the scalar potential have an accidental global symmetry that is spontaneously broken, providing a pseudo-Goldstone boson that is identified as the inflaton. The S3 symmetry restricts both the form of the inflaton potential and the couplings of the inflaton field to the waterfall fields responsible for the end of inflation. We identify viable points in the model parameter space. Although the power in tensor modes is small in most of the parameter space of the model, we identify parameter choices that yield potentially observable values of r without super-Planckian initial values of the inflaton field.
Trees, bialgebras and intrinsic numerical algorithms

NASA Technical Reports Server (NTRS)

Crouch, Peter; Grossman, Robert; Larson, Richard

1990-01-01

Preliminary work about intrinsic numerical integrators evolving on groups is described. Fix a finite dimensional Lie group G; let g denote its Lie algebra, and let Y(sub 1),...,Y(sub N) denote a basis of g. A class of numerical algorithms is presented that approximate solutions to differential equations evolving on G of the form: dot-x(t) = F(x(t)), x(0) = p is an element of G. The algorithms depend upon constants c(sub i) and c(sub ij), for i = 1,...,k and j is less than i. The algorithms have the property that if the algorithm starts on the group, then it remains on the group. In addition, they also have the property that if G is the abelian group R(N), then the algorithm becomes the classical Runge-Kutta algorithm. The Cayley algebra generated by labeled, ordered trees is used to generate the equations that the coefficients c(sub i) and c(sub ij) must satisfy in order for the algorithm to yield an rth order numerical integrator and to analyze the resulting algorithms.
Quantum dressing orbits on compact groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Šťovíček, Pavel

1993-02-01

The quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum Iwasawa decompositon in the general case. Quantum dressing orbits are described explicitly as *-algebras. The dual coalgebras consisting of differential operators are related to the quantum Weyl elements. Besides, the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible *-representations of the algebras of quantum functions. Representation spaces then consist of analytic functions on classical phase spaces. These representations are also interpreted in the framework of quantization in the spirit of Berezin applied to symplectic leaves on classical compact groups. Convenient “coherent states” are introduced and a correspondence between classical and quantum observables is given.
Low-dimensional representations of the three component loop braid group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruillard, Paul; Chang, Liang; Hong, Seung-Moon

2015-11-01

Motivated by physical and topological applications, we study representations of the group LB3 o motions of 3 unlinked oriented circles in R3. Our point of view is to regard the three strand braid group B3 as a subgroup of LB3 and study the problem of extending B3 representations. We introduce the notion of a standard extension and characterize B3 represenations admiting such an extension. In particular we show, using a classification result of Tuba and Wenzl, that every irreducible B3 representation of dimension at most 5 has a (standard) extension. We show that this result is sharp by exhibiting anmore » irreducible 6-dimensional B3 representation that has no extension (standard or otherwise). We obtain complete classifications of (1) irreducible 2-dimensional LB3 representations (2) extensions of irreducible B3 representations and (3) irreducible LB3 representations whose restriction to B3 has abelian image.« less
Nonlocal conservation laws of the constant astigmatism equation

NASA Astrophysics Data System (ADS)

Hlaváč, Adam; Marvan, Michal

2017-03-01

For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.
New scheme for braiding Majorana fermions.

PubMed

Wu, Long-Hua; Liang, Qi-Feng; Hu, Xiao

2014-12-01

Non-Abelian statistics can be achieved by exchanging two vortices in topological superconductors with each grabbing a Majorana fermion (MF) as zero-energy quasi-particle at the cores. However, in experiments it is difficult to manipulate vortices. In the present work, we propose a way to braid MFs without moving vortices. The only operation required in the present scheme is to turn on and off local gate voltages, which liberates a MF from its original host vortex and transports it along the prepared track. We solve the time-dependent Bogoliubov-de Gennes equation numerically, and confirm that the MFs are protected provided the switching of gate voltages for exchanging MFs are adiabatic, which takes only several nano seconds given reasonable material parameters. By monitoring the time evolution of MF wave-functions, we show that non-Abelian statistics is achieved.
An infinite swampland of U(1) charge spectra in 6D supergravity theories

NASA Astrophysics Data System (ADS)

Taylor, Washington; Turner, Andrew P.

2018-06-01

We analyze the anomaly constraints on 6D supergravity theories with a single abelian U(1) gauge factor. For theories with charges restricted to q = ±1 , ±2 and no tensor multiplets, anomaly-free models match those models that can be realized from F-theory compactifications almost perfectly. For theories with tensor multiplets or with larger charges, the F-theory constraints are less well understood. We show, however, that there is an infinite class of distinct massless charge spectra in the "swampland" of theories that satisfy all known quantum consistency conditions but do not admit a realization through F-theory or any other known approach to string compactification. We also compare the spectra of charged matter in abelian theories with those that can be realized from breaking nonabelian SU(2) and higher rank gauge symmetries.
Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures.

PubMed

Wan, Zhong; Kazakov, Aleksandr; Manfra, Michael J; Pfeiffer, Loren N; West, Ken W; Rokhinson, Leonid P

2015-06-11

Search for Majorana fermions renewed interest in semiconductor-superconductor interfaces, while a quest for higher-order non-Abelian excitations demands formation of superconducting contacts to materials with fractionalized excitations, such as a two-dimensional electron gas in a fractional quantum Hall regime. Here we report induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures and development of highly transparent semiconductor-superconductor ohmic contacts. Supercurrent with characteristic temperature dependence of a ballistic junction has been observed across 0.6 μm, a regime previously achieved only in point contacts but essential to the formation of well separated non-Abelian states. High critical fields (>16 T) in NbN contacts enables investigation of an interplay between superconductivity and strongly correlated states in a two-dimensional electron gas at high magnetic fields.
Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures

PubMed Central

Wan, Zhong; Kazakov, Aleksandr; Manfra, Michael J.; Pfeiffer, Loren N.; West, Ken W.; Rokhinson, Leonid P.

2015-01-01

Search for Majorana fermions renewed interest in semiconductor–superconductor interfaces, while a quest for higher-order non-Abelian excitations demands formation of superconducting contacts to materials with fractionalized excitations, such as a two-dimensional electron gas in a fractional quantum Hall regime. Here we report induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures and development of highly transparent semiconductor–superconductor ohmic contacts. Supercurrent with characteristic temperature dependence of a ballistic junction has been observed across 0.6 μm, a regime previously achieved only in point contacts but essential to the formation of well separated non-Abelian states. High critical fields (>16 T) in NbN contacts enables investigation of an interplay between superconductivity and strongly correlated states in a two-dimensional electron gas at high magnetic fields. PMID:26067452
Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lahiri, Sayantani, E-mail: sayantani.lahiri@gmail.com

2017-01-01

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by amore » non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.« less
The NNLO QCD soft function for 1-jettiness

NASA Astrophysics Data System (ADS)

Campbell, John M.; Ellis, R. Keith; Mondini, Roberto; Williams, Ciaran

2018-03-01

We calculate the soft function for the global event variable 1-jettiness at next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the non-Abelian contribution, which, unlike the Abelian part, is not determined by the next-to-leading order result. The calculation uses the known general forms for the emission of one and two soft partons and is performed using a sector-decomposition method that is spelled out in detail. Results are presented in the form of numerical fits to the 1-jettiness soft function for LHC kinematics (as a function of the angle between the incoming beams and the final-state jet) and for generic kinematics (as a function of three independent angles). These fits represent one of the needed ingredients for NNLO calculations that use the N-jettiness event variable to handle infrared singularities.
Non-abelian factorisation for next-to-leading-power threshold logarithms

NASA Astrophysics Data System (ADS)

Bonocore, D.; Laenen, E.; Magnea, L.; Vernazza, L.; White, C. D.

2016-12-01

Soft and collinear radiation is responsible for large corrections to many hadronic cross sections, near thresholds for the production of heavy final states. There is much interest in extending our understanding of this radiation to next-to-leading power (NLP) in the threshold expansion. In this paper, we generalise a previously proposed all-order NLP factorisation formula to include non-abelian corrections. We define a nonabelian radiative jet function, organising collinear enhancements at NLP, and compute it for quark jets at one loop. We discuss in detail the issue of double counting between soft and collinear regions. Finally, we verify our prescription by reproducing all NLP logarithms in Drell-Yan production up to NNLO, including those associated with double real emission. Our results constitute an important step in the development of a fully general resummation formalism for NLP threshold effects.
Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories

NASA Astrophysics Data System (ADS)

Canfora, Fabrizio; Giacomini, Alex; Oliva, Julio

2010-08-01

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti-de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.
Wire constructions of Abelian topological phases in three or more dimensions

NASA Astrophysics Data System (ADS)

Iadecola, Thomas; Neupert, Titus; Chamon, Claudio; Mudry, Christopher

2016-05-01

Coupled-wire constructions have proven to be useful tools to characterize Abelian and non-Abelian topological states of matter in two spatial dimensions. In many cases, their success has been complemented by the vast arsenal of other theoretical tools available to study such systems. In three dimensions, however, much less is known about topological phases. Since the theoretical arsenal in this case is smaller, it stands to reason that wire constructions, which are based on one-dimensional physics, could play a useful role in developing a greater microscopic understanding of three-dimensional topological phases. In this paper, we provide a comprehensive strategy, based on the geometric arrangement of commuting projectors in the toric code, to generate and characterize coupled-wire realizations of strongly interacting three-dimensional topological phases. We show how this method can be used to construct pointlike and linelike excitations, and to determine the topological degeneracy. We also point out how, with minor modifications, the machinery already developed in two dimensions can be naturally applied to study the surface states of these systems, a fact that has implications for the study of surface topological order. Finally, we show that the strategy developed for the construction of three-dimensional topological phases generalizes readily to arbitrary dimensions, vastly expanding the existing landscape of coupled-wire theories. Throughout the paper, we discuss Zm topological order in three and four dimensions as a concrete example of this approach, but the approach itself is not limited to this type of topological order.
N = (2,0) self-dual non-Abelian tensor multiplet in D = 3 + 3 generates N = (1,1) self-dual systems in D = 2 + 2

NASA Astrophysics Data System (ADS)

Nishino, Hitoshi; Rajpoot, Subhash

2018-03-01

We formulate an N = (2 , 0) system in D = 3 + 3 dimensions consisting of a Yang-Mills (YM)-multiplet (ˆ μ ˆ IA, λˆI), a self-dual non-Abelian tensor multiplet (ˆ μ ˆ ν ˆ IB, χˆI ,φˆI), and an extra vector multiplet (C ˆ μ ˆ IC, ρˆI). We next perform the dimensional reductions of this system into D = 2 + 2, and obtain N = (1 , 1) systems with a self-dual YM-multiplet (AIμ ,λI), a self-dual tensor multiplet (BIμν , χI , φI), and an extra vector multiplet (CIμ , ρI). In D = 2 + 2, we reach two distinct theories: 'Theory-I' and 'Theory-II'. The former has the self-dual field-strength Hμν(+)I of CIμ already presented in our recent paper, while the latter has anti-self-dual field strength Hμν(-)I. As an application, we show that Theory-II actually generates supersymmetric-KdV equations in D = 1 + 1. Our result leads to a new conclusion that the D = 3 + 3 theory with non-Abelian tensor multiplet can be a 'Grand Master Theory' for self-dual multiplet and self-dual YM-multiplet in D = 2 + 2, that in turn has been conjectured to be the 'Master Theory' for all supersymmetric integrable theories in D ≤ 3.
Scalar formalism for non-Abelian gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hostler, L.C.

1986-09-01

The gauge field theory of an N-italic-dimensional multiplet of spin- 1/2 particles is investigated using the Klein--Gordon-type wave equation )Pi x (1+i-italicsigma) x Pi+m-italic/sup 2/)Phi = 0, Pi/sub ..mu../equivalentpartial/partiali-italicx-italic/sub ..mu../-e-italicA-italic/sub ..mu../, investigated before by a number of authors, to describe the fermions. Here Phi is a 2 x 1 Pauli spinor, and sigma repesents a Lorentz spin tensor whose components sigma/sub ..mu..//sub ..nu../ are ordinary 2 x 2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. Themore » equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum tau-functions, tau(2,1, xxx 3 xxx)equivalent<0-chemically bondT-italic(Psi/sub in/(2) Psi-bar/sub in/(1) xxx A-italic/sub ..mu../(3)/sub in/ xxx S-italic)chemically bond0->, where Psi/sub in/ is a Heisenberg operator belonging to a 4N-italic x 1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics.« less
Evaluation of the sealing ability of gutta-percha and thermoplastic synthetic polymer-based systems along the root canals through the glucose penetration model.

PubMed

Kaya, B Ureyen; Kececi, Ayşe Diljin; Belli, S

2007-12-01

To compare the sealing ability of gutta-percha and thermoplastic synthetic polymer-based systems along the root canals using a recently introduced glucose penetration model. Premolars (n = 156) instrumented to an apical size of .06/40 were divided into 12 experimental and 2 control groups. The root canals were filled with either gutta-percha (groups 1-6) or Resilon (groups 7-12) core materials combined with AH Plus (groups 1, 4, 7, 0), Ketac Endo (groups 1, 5, 8, 11), or Epiphany (groups 2, 6, 9, 12), using cold lateral compaction (groups 1-3, 7-9) or System B with Obtura II (groups 4-6, 10-12). The leaked glucose concentration was measured spectrophotometrically at 1, 8, 15, 22, and 30 days. Percentage leaking of each group was also calculated. Data were recorded as mmol/L and statistically analyzed with Kruskal-Wallis and Mann-Whitney U tests (P = .05). Throughout the experimental period Resilon/Ketac-Endo/cold lateral compaction (group 8) showed the highest mean cumulative glucose penetration (mmol/L) (17.27 +/- 10.32), whereas Resilon/AH Plus/cold lateral compaction (group 7) had the least (3.36 +/- 4.65) (P < .05). At the 30(th) day, the least leaking percentage was observed in gutta-percha, Epiphany/cold lateral compaction (group 3). Glucose penetration was affected by the obturation technique in some groups. Ketac-Endo either with gutta-percha (group 2) or Resilon (group 8) indicated significantly less glucose penetration in warm technique, whereas gutta-percha/Epiphany (group 3) had significantly less glucose penetration in cold technique (P < .05). All material/technique combinations allowed glucose penetration. Gutta-percha/AH Plus combinations allowed similar patterns of glucose penetration to Resilon/Epiphany combinations.

Constructing topological models by symmetrization: A projected entangled pair states study

NASA Astrophysics Data System (ADS)

Fernández-González, Carlos; Mong, Roger S. K.; Landon-Cardinal, Olivier; Pérez-García, David; Schuch, Norbert

2016-10-01

Symmetrization of topologically ordered wave functions is a powerful method for constructing new topological models. Here we study wave functions obtained by symmetrizing quantum double models of a group G in the projected entangled pair states (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group G ˜ which is always non-Abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wave functions in the same phase as the double model of G ˜. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of G ˜.
Staggered Orbital Currents in the Half-Filled Two-Leg Ladder

NASA Astrophysics Data System (ADS)

Fjaerestad, J. O.; Marston, Brad; Sudbo, A.

2002-03-01

We present strong analytical and numerical evidence for the existence of a staggered flux (SF) phase in the half-filled two-leg ladder, with true long-range order in the counter-circulating currents. Using abelian bosonization with a careful treatment of the Klein factors, we show that a certain phase of the half-filled ladder, previously identified as having spin-Peierls order, instead exhibits staggered orbital currents with no dimerization.(J. O. Fjærestad and J. B. Marston, cond- mat/0107094.) This result, combined with a weak-coupling renormalization-group analysis, implies that the SF phase exists in a region of the phase diagram of the half-filled t-U-V-J ladder. Using the density-matrix renormalization-group (DMRG) approach generalized to complex-valued wavefunctions, we demonstrate that the SF phase exhibits robust currents at intermediate values of the interaction strengths.
Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay constant

NASA Astrophysics Data System (ADS)

Kim, Jihn E.; Nam, Soonkeon; Semetzidis, Yannis K.

2018-01-01

Pseudoscalars appearing in particle physics are reviewed systematically. From the fundamental point of view at an ultraviolet completed theory, they can be light if they are realized as pseudo-Goldstone bosons of some spontaneously broken global symmetries. The spontaneous breaking scale is parametrized by the decay constant f. The global symmetry is defined by the lowest order terms allowed in the effective theory consistent with the gauge symmetry in question. Since any global symmetry is known to be broken at least by quantum gravitational effects, all pseudoscalars should be massive. The mass scale is determined by f and the explicit breaking terms ΔV in the effective potential and also anomaly terms ΔΛG4 for some non-Abelian gauge groups G. The well-known example by non-Abelian gauge group breaking is the potential for the “invisible” QCD axion, via the Peccei-Quinn symmetry, which constitutes a major part of this review. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms ΔV in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a “quintessential axion.” In general, (ΔV )1/4 is considered to be smaller than f, and hence the pseudo-Goldstone boson mass scales are considered to be smaller than the decay constants. In such a case, the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model, which is known as “natural inflation.” We review all these ideas in the bosonic collective motion framework.
Non-Abelian semilocal strings in N=2 supersymmetric QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shifman, M.; Yung, A.; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300

2006-06-15

We consider a benchmark bulk theory in four dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N{sub f} flavors of fundamental matter hypermultiplets (quarks). The nature of the Bogomol'nyi-Prasad-Sommerfield (BPS) strings in this benchmark theory crucially depends on N{sub f}. If N{sub f}{>=}N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N{sub f}>N these strings become semilocal, developing additional moduli {rho} related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N{sub f}=3, 4 as an example, we derive an effective low-energy theory on themore » (two-dimensional) string world sheet. Our derivation is field theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz, and solve it at large {rho}. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is an N=2 supersymmetric U(1) gauge theory with N positively and N{sub e}=N{sub f}-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided that the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if {delta}m{sub AB}{ne}0.« less
Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benini, Marco, E-mail: mbenini87@gmail.com, E-mail: mbenini@uni-potsdam.de

Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincaré duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor.more » The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincaré duality for the new cohomology groups.« less
Dynamical theory of dense groups of galaxies

NASA Technical Reports Server (NTRS)

Mamon, Gary A.

1990-01-01

It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups.
Curved noncommutative tori as Leibniz quantum compact metric spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latrémolière, Frédéric, E-mail: frederic@math.du.edu

We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Irreversibility and higher-spin conformal field theory

NASA Astrophysics Data System (ADS)

Anselmi, Damiano

2000-08-01

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.
New developments in the theoretical treatment of low dimensional strongly correlated systems.

PubMed

James, Andrew J A; Konik, Robert M; Lecheminant, Philippe; Robinson, Neil; Tsvelik, Alexei M

2017-10-09

We review two important non-perturbative approaches for extracting the physics of low- dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of confor- mal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symme- tries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chro- modynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics. © 2017 IOP Publishing Ltd.
V-V compact group of galaxies

NASA Technical Reports Server (NTRS)

Bahcall, N.

1984-01-01

A search for X-ray emission from five compact groups of galaxies with the Einstein Observatory revealed detections from three groups. Soft, extended X-ray emission was observed in Stephan's Quintet which is most likely caused by hot intracluster gas. This provides evidence for dynamical interaction among the group galaxies. X-ray emission from the group Arp 330 may also originate in hot intracluster gas. Stephan's Quintet and Arp 330 have the largest velocity dispersions among the groups studied suggesting a correlation between high velocity and the release (or properties) of hot gas. X-ray emission from Arp 318 may originate in its member galaxies.
Rotating hairy black holes.

PubMed

Kleihaus, B; Kunz, J

2001-04-23

We construct stationary black-hole solutions in SU(2) Einstein-Yang-Mills theory which carry angular momentum and electric charge. Possessing nontrivial non-Abelian magnetic fields outside their regular event horizon, they represent nonperturbative rotating hairy black holes.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.

Compact groups of galaxies provide a unique environment to study the evolution of galaxies amid frequent gravitational encounters. These nearby groups have conditions similar to those in the earlier universe when galaxies were assembled and give us the opportunity to witness hierarchical formation in progress. To understand how the compact group environment affects galaxy evolution, we examine the gas and dust in these groups. We present new single-dish GBT neutral hydrogen (H i) observations of 30 compact groups and define a new way to quantify the group H i content as the H i-to-stellar mass ratio of the group asmore » a whole. We compare the H i content with mid-IR indicators of star formation and optical [g − r] color to search for correlations between group gas content and star formation activity of individual group members. Quiescent galaxies tend to live in H i-poor groups, and galaxies with active star formation are more commonly found in H i-rich groups. Intriguingly, we also find “rogue” galaxies whose star formation does not correlate with group H i content. In particular, we identify three galaxies (NGC 2968 in RSCG 34, KUG 1131+202A in RSCG 42, and NGC 4613 in RSCG 64) whose mid-IR activity is discrepant with the H i. We speculate that this mismatch between mid-IR activity and H i content is a consequence of strong interactions in this environment that can strip H i from galaxies and abruptly affect star formation. Ultimately, characterizing how and on what timescales the gas is processed in compact groups will help us understand the interstellar medium in complex, dense environments similar to the earlier universe.« less
K-theory of locally finite graph C∗-algebras

NASA Astrophysics Data System (ADS)

Iyudu, Natalia

2013-09-01

We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).
Five-dimensional fermionic Chern-Simons theory

NASA Astrophysics Data System (ADS)

Bak, Dongsu; Gustavsson, Andreas

2018-02-01

We study 5d fermionic CS theory with a fermionic 2-form gauge potential. This theory can be obtained from 5d maximally supersymmetric YM theory by performing the maximal topological twist. We put the theory on a five-manifold and compute the partition function. We find that it is a topological quantity, which involves the Ray-Singer torsion of the five-manifold. For abelian gauge group we consider the uplift to the 6d theory and find a mismatch between the 5d partition function and the 6d index, due to the nontrivial dimensional reduction of a selfdual two-form gauge field on a circle. We also discuss an application of the 5d theory to generalized knots made of 2d sheets embedded in 5d.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Ni, Xiaotong; Van den Nest, Maarten; Buerschaper, Oliver

We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of single-qubit operators drawn from the group 〈αI, X, S〉, where α = e{sup iπ/4} and S = diag(1, i). We provide techniques to efficiently compute various properties related to bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians, etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular, we give examplesmore » of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that support non-Abelian anyons.« less
Locality-preserving logical operators in topological stabilizer codes

NASA Astrophysics Data System (ADS)

Webster, Paul; Bartlett, Stephen D.

2018-01-01

Locality-preserving logical operators in topological codes are naturally fault tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological stabilizer codes. In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators. We also present examples of how our procedure applies to codes with different boundary conditions, including color codes and toric codes, as well as more general codes such as Abelian quantum double models and codes with fermionic excitations in more than two dimensions.
ROSAT: X ray survey of compact groups

NASA Technical Reports Server (NTRS)

Vangorkom, Jacqueline

1993-01-01

This is the final technical report on grant NAG5-1954, which was awarded under the NASA ROSAT Guest Investigator Program to Columbia University. This grant was awarded for a number of projects on two rather different topics: (1) an x-ray survey of compact groups of galaxies; and (2) the fate of gas in merging galaxies. Progress made in these projects is presented.
How serious a problem is subsoil compaction in the Netherlands? A survey based on probability sampling

NASA Astrophysics Data System (ADS)

Brus, Dick J.; van den Akker, Jan J. H.

2018-02-01

Although soil compaction is widely recognized as a soil threat to soil resources, reliable estimates of the acreage of overcompacted soil and of the level of soil compaction parameters are not available. In the Netherlands data on subsoil compaction were collected at 128 locations selected by stratified random sampling. A map showing the risk of subsoil compaction in five classes was used for stratification. Measurements of bulk density, porosity, clay content and organic matter content were used to compute the relative bulk density and relative porosity, both expressed as a fraction of a threshold value. A subsoil was classified as overcompacted if either the relative bulk density exceeded 1 or the relative porosity was below 1. The sample data were used to estimate the means of the two subsoil compaction parameters and the overcompacted areal fraction. The estimated global means of relative bulk density and relative porosity were 0.946 and 1.090, respectively. The estimated areal fraction of the Netherlands with overcompacted subsoils was 43 %. The estimates per risk map unit showed two groups of map units: a low-risk group (units 1 and 2, covering only 4.6 % of the total area) and a high-risk group (units 3, 4 and 5). The estimated areal fraction of overcompacted subsoil was 0 % in the low-risk unit and 47 % in the high-risk unit. The map contains no information about where overcompacted subsoils occur. This was caused by the poor association of the risk map units 3, 4 and 5 with the subsoil compaction parameters and subsoil overcompaction. This can be explained by the lack of time for recuperation.
Entanglement of Distillation for Lattice Gauge Theories.

PubMed

Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B; Verstraete, Frank

2016-09-23

We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
The NNLO QCD soft function for 1-jettiness

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campbell, John M.; Ellis, R. Keith; Mondini, Roberto

We calculate the soft function for the global event variable 1-jettiness at next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the non-Abelian contribution, which, unlike the Abelian part, is not determined by the next-to-leading order result. The calculation uses the known general forms for the emission of one and two soft partons and is performed using a sector-decomposition method that is spelled out in detail. Results are presented in the form of numerical fits to the 1-jettiness soft function for LHC kinematics (as a function of the angle between the incoming beams and the final-state jet) and for genericmore » kinematics (as a function of three independent angles). These fits represent one of the needed ingredients for NNLO calculations that use the N-jettiness event variable to handle infrared singularities.« less

Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model

NASA Astrophysics Data System (ADS)

Borcherding, Daniel; Frahm, Holger

2018-05-01

The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both spin and SU(N f ) orbital degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations (Tsvelik 2014 Phys. Rev. Lett. 113 066401). From their quantum dimension they are identified as spin- anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.
Thermodynamics of dyonic black holes with Thurston horizon geometries

NASA Astrophysics Data System (ADS)

Bravo-Gaete, Moisés; Hassaïne, Mokhtar

2018-01-01

In five dimensions, we consider a model described by the Einstein gravity with a source given by a scalar field and various Abelian gauge fields with dilatoniclike couplings. For this model, we are able to construct two dyonic black holes whose three-dimensional horizons are modeled by two nontrivial homogeneous Thurston's geometries. The dyonic solutions are of Lifshitz type with an arbitrary value of the dynamical exponent. In fact, the first gauge field ensures the anisotropy asymptotic while the remaining Abelian fields sustain the electric and magnetic charges. Using the Hamiltonian formalism, the mass, the electric, and magnetic charges are explicitly computed. Interestingly enough, the dyonic solutions behave like Chern-Simons vortices in the sense that their electric and magnetic charges turn to be proportional. The extension with an hyperscaling violating factor is also scrutinized where we notice that for specific values of the violating factor, purely magnetic solutions are possible.
The NNLO QCD soft function for 1-jettiness

DOE PAGES

Campbell, John M.; Ellis, R. Keith; Mondini, Roberto; ...

2018-03-19

We calculate the soft function for the global event variable 1-jettiness at next-to-next-to-leading order (NNLO) in QCD. We focus specifically on the non-Abelian contribution, which, unlike the Abelian part, is not determined by the next-to-leading order result. The calculation uses the known general forms for the emission of one and two soft partons and is performed using a sector-decomposition method that is spelled out in detail. Results are presented in the form of numerical fits to the 1-jettiness soft function for LHC kinematics (as a function of the angle between the incoming beams and the final-state jet) and for genericmore » kinematics (as a function of three independent angles). These fits represent one of the needed ingredients for NNLO calculations that use the N-jettiness event variable to handle infrared singularities.« less
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zohar, Erez, E-mail: erez.zohar@mpq.mpg.de; Wahl, Thorsten B.; Burrello, Michele, E-mail: michele.burrello@mpq.mpg.de

Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of amore » simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.« less
Classical simulation of quantum error correction in a Fibonacci anyon code

NASA Astrophysics Data System (ADS)

Burton, Simon; Brell, Courtney G.; Flammia, Steven T.

2017-02-01

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128 ×128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for Abelian and (nonuniversal) non-Abelian anyon models.
Duality and 'particle' democracy

NASA Astrophysics Data System (ADS)

Castellani, Elena

2017-08-01

Weak/strong duality is usually accompanied by what seems a puzzling ontological feature: the fact that under this kind of duality what is viewed as 'elementary' in one description gets mapped to what is viewed as 'composite' in the dual description. This paper investigates the meaning of this apparent 'particle democracy', as it has been called, by adopting an historical approach. The aim is to clarify the nature of the correspondence between 'dual particles' in the light of a historical analysis of the developments of the idea of weak/strong duality, starting with Dirac's electric-magnetic duality and its successive generalizations in the context of (Abelian and non-Abelian) field theory, to arrive at its first extension to string theory. This analysis is then used as evidential basis for discussing the 'elementary/composite' divide and, after taking another historical detour by analyzing an instructive analogy case (DHS duality and related nuclear democracy), drawing some conclusions on the particle-democracy issue.
Edge-mode superconductivity in a two-dimensional topological insulator.

PubMed

Pribiag, Vlad S; Beukman, Arjan J A; Qu, Fanming; Cassidy, Maja C; Charpentier, Christophe; Wegscheider, Werner; Kouwenhoven, Leo P

2015-07-01

Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which have been predicted to occur in the surface states of three-dimensional systems, in the edge states of two-dimensional systems, and in one-dimensional wires. Localized Majorana zero-modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing. Here, we report superconductivity induced in the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator. Using superconducting quantum interference we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the two-dimensional topological phase. These experiments establish InAs/GaSb as a promising platform for the confinement of Majoranas into localized states, enabling future investigations of non-Abelian statistics.
A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165
Counting surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group with motivations from string theory and QFT

NASA Astrophysics Data System (ADS)

Bibak, Khodakhast; Kapron, Bruce M.; Srinivasan, Venkatesh

2016-09-01

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT). Recently, Koch et al. (2013) [12] gave a refined formula for counting ribbon graphs and discussed its applications to several physics problems. An important factor in this formula is the number of surface-kernel epimorphisms from a co-compact Fuchsian group to a cyclic group. The aim of this paper is to give an explicit and practical formula for the number of such epimorphisms. As a consequence, we obtain an 'equivalent' form of Harvey's famous theorem on the cyclic groups of automorphisms of compact Riemann surfaces. Our main tool is an explicit formula for the number of solutions of restricted linear congruence recently proved by Bibak et al. using properties of Ramanujan sums and of the finite Fourier transform of arithmetic functions.
Sintering of compacts of UN, (U,Pu)N, and PuN

DOEpatents

Tennery, V.J.; Godfrey, T.G.; Bomar, E.S.

1973-10-16

>A method is provided for preparing a densified compact of a metal nitride selected from the group consisting of UN, (U,Pu)N, and PuN which comprises heating a green compact of at least one selected nitride in the mononitride single-phase region, as displayed by a phase diagram of the mononitride of said compact, in a nitrogen atmosphere at a pressure of nitrogen less than 760 torr. At a given temperature, this process produces a singlephase structure and a maximal sintered density as measured by mercury displacement. (Official Gazette)
X-ray emission from Stephan's Quintet and other compact groups

NASA Technical Reports Server (NTRS)

Bahcall, N. A.; Harris, D. E.; Rood, H. J.

1984-01-01

A search for X-ray emission from five compact groups of galaxies with the Einstein Observatory revealed detections from three groups. Soft, extended X-ray emission was observed in Stephan's Quintet, which is most likely caused by hot intracluster gas. This provides evidence for dynamical interaction among the group galaxies. X-ray emission from the group Arp 330 may also originate in hot intracluster gas. Stephan's Quintet and Arp 330 have the largest velocity dispersions among the groups studied, suggesting a correlation between high velocity and the release (or properties) of hot gas. X-ray emission from Arp 318 may originate in its member galaxies.
Wireless majorana fermions: from magnetic tunability to braiding (Conference Presentation)

NASA Astrophysics Data System (ADS)

Fatin, Geoffrey L.; Matos-Abiague, Alex; Scharf, Benedikt; Zutic, Igor

2016-10-01

In condensed-matter systems Majorana bound states (MBSs) are emergent quasiparticles with non-Abelian statistics and particle-antiparticle symmetry. While realizing the non-Abelian braiding statistics under exchange would provide both an ultimate proof for MBS existence and the key element for fault-tolerant topological quantum computing, even theoretical schemes imply a significant complexity to implement such braiding. Frequently examined 1D superconductor/semiconductor wires provide a prototypical example of how to produce MBSs, however braiding statistics are ill-defined in 1D and complex wire networks must be used. By placing an array of magnetic tunnel junctions (MTJs) above a 2D electron gas formed in a semiconductor quantum well grown on the surface of an s-wave superconductor, we have predicted the existence of highly tunable zero-energy MBSs and have proposed a novel scheme by which MBSs could be exchanged [1]. This scheme may then be used to demonstrate the states' non-Abelian statistics through braiding. The underlying magnetic textures produced by MTJ array provides a pseudo-helical texture which allows for highly-controllable topological phase transitions. By defining a local condition for topological nontriviality which takes into account the local rotation of magnetic texture, effective wire geometries support MBS formation and permit their controlled movement in 2D by altering the shape and orientation of such wires. This scheme then overcomes the requirement for a network of physical wires in order to exchange MBSs, allowing easier manipulation of such states. [1] G. L. Fatin, A. Matos-Abiague, B. Scharf, and I. Zutic, arXiv:1510.08182, preprint.
VizieR Online Data Catalog: HCG and RSCG compact group galaxies with WISE (Zucker+, 2016)

NASA Astrophysics Data System (ADS)

Zucker, C.; Walker, L. M.; Johnson, K.; Gallagher, S.; Alatalo, K.; Tzanavaris, P.

2016-07-01

For this study, we draw our sample from groups in the HCG catalog (Hickson 1982, VII/213) and the Redshift Survey Compact Group catalog (RSCG; Barton et al. 1996AJ....112..871B). We utilize new ALLWISE coadds from Lang (unWISE; 2014AJ....147..108L), which preserve the native resolution of the raw frames (~6.1", 6.4", 6.5" and 12.0" for bands W1, W2, W3, and W4). (1 data file).
Compact earth stations, hubs for energy industry expanding

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shimabukuro, T.

1992-02-01

That paper reports that advances in gallium arsenide (GaAs) technology, monolithic microwave integrated circuits (MMIC) and large scale integrated (VLSF) circuits, have contributed to the mass production of very reliable small aperture terminals (VSATs). Less publicized, but equally important to multinational energy organizations, are recent developments in compact earth station design and solid-state hubs for VSAT networks made possible by the new technology. Many applications are suited for the energy industry that involve compact earth station terminals and hubs. The first group of applications describes the use of GTE's ACES earth station for the Zaire Gulf Oil Co. in Zairemore » and for AMOCO in Trinidad. The second group of applications describes the compact hub for VSAT networks, which could potentially have a number of data communication uses in the energy industry, such as, IBM/SNA, X.25, or supervisory control an data acquisition (SCADA) applications.« less
The new electromagnetic tetrads, infinite tetrad nesting and the non-trivial emergence of complex numbers in real theories of gravitation

NASA Astrophysics Data System (ADS)

Garat, Alcides

How complex numbers get into play in a non-trivial way in real theories of gravitation is relevant since in a unified structure they should be able to relate in a natural way with quantum theories. For a long time this issue has been lingering on both relativistic formulations and quantum theories. We will analyze this fundamental subject under the light of new group isomorphism theorems linking local internal groups of transformations and local groups of spacetime transformations. The bridge between these two kinds of transformations is represented by new tetrads introduced previously. It is precisely through these local tetrad structures that we will provide a non-trivial answer to this old issue. These new tetrads have two fundamental building components, the skeletons and the gauge vectors. It is these constructive elements that provide the mathematical support that allows to prove group isomorphism theorems. In addition to this, we will prove a unique new property, the infinite tetrad nesting, alternating the nesting with non-Abelian tetrads in the construction of the tetrad gauge vectors. As an application we will demonstrate an alternative proof of a new group isomorphism theorem.
A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

NASA Astrophysics Data System (ADS)

Taylor, Washington; Wang, Yi-Nan

2016-01-01

We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ˜ 1048. The distribution of bases peaks around h 1,1 ˜ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in h 1,1 of the threefold base. Typical bases have ˜ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) × SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) × SU(2) is the third most common connected two-factor product group, following SU(2) × SU(2) and G 2 × SU(2), which arise more frequently.
A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

DOE PAGES

Taylor, Washington; Wang, Yi-Nan

2016-01-22

Here, we use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ~ 10 48. Moreover, the distribution of bases peaks around h 1,1 ~ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We also find that the number of non-Higgsable gauge group factors grows roughly linearly in h 1,1 of the threefold base. Typical basesmore » have ~ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) x SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected two-factor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.« less
Modular Extensions of Unitary Braided Fusion Categories and 2+1D Topological/SPT Orders with Symmetries

NASA Astrophysics Data System (ADS)

Lan, Tian; Kong, Liang; Wen, Xiao-Gang

2017-04-01

A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category E. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry E are classified, up to {E_8} quantum Hall states, by the unitary modular tensor categories C over E and the modular extensions of each C. In the case C=E, we prove that the set M_{ext}(E) of all modular extensions of E has a natural structure of a finite abelian group. We also prove that the set M_{ext}(C) of all modular extensions of E, if not empty, is equipped with a natural M_{ext}(C)-action that is free and transitive. Namely, the set M_{ext}(C) is an M_{ext}(E)-torsor. As special cases, we explain in detail how the group M_{ext}(E) recovers the well-known group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16 fold ways. We also discuss briefly the behavior of the group M_{ext}(E) under the symmetry-breaking processes and its relation to Witt groups.
Evaluation of canal filling after using two warm vertical gutta-percha compaction techniques in vivo: a preliminary study.

PubMed

Venturi, M

2006-07-01

To evaluate the quality of root canal filling when comparing two warm gutta-percha filling techniques in vivo. Human teeth were randomly divided into two equal groups, with 30 canals each. The root canals were shaped by hand and ProFile 0.04 rotary instruments to size 20-40 at the end-point and then filled with gutta-percha cones and AH-Plus. In group A, a traditional warm vertical compaction technique was performed using the Touch'n Heat, and back-filling with the Obtura II. In group B, a modified warm vertical compaction technique was used: small amounts of gutta-percha were removed, and the remaining most apical 3 mm were compacted with a 1 mm movement; then thermomechanical back-filling was performed. The teeth were extracted, stored in dye, cleared, and the distance between the apex and apical limit of the filling, linear dye penetration, and voids were measured from the buccal, lingual, mesial and distal perspective. The homogeneity of variance and means was verified using Levene's test and t-test. ANOVA and Dunnett post hoc test were used to establish the significance and to analyse the effects through multiple comparisons. Compared with the specimens of group A, the specimens of group B exhibited less mean linear dye penetration (P < 0.05), smaller void length (P < or = 0.05) and maximal width (P < or = 0.05) when examined in all four views, and a more precise filling when viewed from the buccal aspect (P < 0.05). The modified warm vertical compaction technique with apical back-filling produced a more effective and precise three-dimensional filling.
Effects of different root canal obturation techniques on bacterial penetration.

PubMed

Yücel, Ali Cağin; Ciftçi, Alper

2006-10-01

The aim of this study was to compare bacterial penetration following obturation with 5 different techniques. This study was performed on 120 teeth including negative control (n = 10), positive control (n = 10), and experimental groups (n = 100). One hundred teeth were randomly divided into 5 groups of 20 teeth each and obturated with System B (Sb), Lateral Compaction (Lc), Thermafil (T), Single ProTaper Gutta-percha (P), and laterally compacted ProTaper Gutta-percha (PLc). Enterococcus faecalis was used for determination of the bacterial penetration. Evaluation was carried out for 60 days. At 30 days, the chi2 test showed that the slowest penetration was observed in Group Sb and Group PLc, which were not significantly different from each other. The fastest penetration in the all experimental groups was observed in Group T and Group P, which were not significantly different from one another. Also, there was no statistically significance difference (P > .05) among all groups at 60 days. It may be concluded that under the conditions of this study System B and laterally compacted ProTaper Gutta-percha prevent bacterial penetration of the root canal at 30 days. Furthermore, there was no difference among obturation techniques at 60 days.

Effects of soap and detergents on skin surface pH, stratum corneum hydration and fat content in infants.

PubMed

Gfatter, R; Hackl, P; Braun, F

1997-01-01

In adults the influence of cleansing preparations on the pH, fat content and hydration of the skin is well documented. Studies in newborn and small infants have not been reported. Our study aimed at examining whether similar effects can be ascertained in infants. Infants without skin disease, aged 2 weeks to 16 months, entered an open, controlled and randomized study. Ten infants each had skin washed with tap water (control group), liquid detergent (pH 5.5), compact detergent (pH 5.5) or alkaline soap (pH 9.5). The pH, fat content and hydration were measured before and 10 min after cleansing. Findings were statistically evaluated by parametric covariance analysis. The skin pH increased from an average of 6.60 after cleansing in all groups. The smallest increase (+0.19) was observed in the control group, the largest (+0.45) after washing with alkaline soap. After treatment with liquid or compact detergent, the increase of the pH was only 0.09 higher than for the control group. In comparison to the compact and liquid detergents, the alkaline soap group had a significantly higher increase in pH. The fat content (mean starting value: 4.34 micrograms/cm2) decreased after washing in all groups; the smallest effect was observed in the control group (decrease of 0.93 micrograms/cm2), the highest for the alkaline soap group (decrease of 4.81 micrograms/cm2). In comparison to the compact and liquid detergents, the alkaline soap group had a higher decrease in fat content. This difference was significant for compact detergents. No statistically significant differences were observed for hydration before versus after washing. Each cleansing agent, even normal tap water, influences the skin surface. The increase of the skin pH irritates the physiological protective 'acid mantle', changes the composition of the cutaneous bacterial flora and the activity of enzymes in the upper epidermis, which have an acid pH optimum. The dissolution of fat from the skin surface may influence the hydration status leading to a dry and squamous skin.
THE MERGER HISTORY, ACTIVE GALACTIC NUCLEUS, AND DWARF GALAXIES OF HICKSON COMPACT GROUP 59

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konstantopoulos, I. S.; Charlton, J. C.; Brandt, W. N.

2012-01-20

Compact group galaxies often appear unaffected by their unusually dense environment. Closer examination can, however, reveal the subtle, cumulative effects of multiple galaxy interactions. Hickson Compact Group (HCG) 59 is an excellent example of this situation. We present a photometric study of this group in the optical (Hubble Space Telescope), infrared (Spitzer), and X-ray (Chandra) regimes aimed at characterizing the star formation and nuclear activity in its constituent galaxies and intra-group medium. We associate five dwarf galaxies with the group and update the velocity dispersion, leading to an increase in the dynamical mass of the group of up to amore » factor of 10 (to 2.8 Multiplication-Sign 10{sup 13} M{sub Sun }), and a subsequent revision of its evolutionary stage. Star formation is proceeding at a level consistent with the morphological types of the four main galaxies, of which two are star-forming and the other are two quiescent. Unlike in some other compact groups, star-forming complexes across HCG 59 closely follow mass-radius scaling relations typical of nearby galaxies. In contrast, the ancient globular cluster populations in galaxies HCG 59A and B show intriguing irregularities, and two extragalactic H II regions are found just west of B. We age-date a faint stellar stream in the intra-group medium at {approx}1 Gyr to examine recent interactions. We detect a likely low-luminosity active galactic nucleus in HCG 59A by its {approx}10{sup 40} erg s{sup -1} X-ray emission; the active nucleus rather than star formation can account for the UV+IR spectral energy distribution. We discuss the implications of our findings in the context of galaxy evolution in dense environments.« less
The Merger History, AGN and Dwarf Galaxies of Hickson Compact Group 59

NASA Technical Reports Server (NTRS)

Konstantopoulos, I. S.; Gallagher, S. C.; Fedotov, K.; Durrell, P. R.; Tzanavaris, P.; Hill, A. R.; Zabludoff, A. I.; Maier, M. L.; Elmegreen, D. M.; Charlton, J. C.;

2011-01-01

Compact group galaxies often appear unaffected by their unusually dense environment. Closer examination can, however, reveal the subtle, cumulative effects of multiple galaxy interactions. Hickson Compact Group (HCG) 59 is an excellent example of this situation. We present a photometric study of this group in the optical (HST), infrared (Spitzer) and X-ray (Chandra) regimes aimed at characterizing the star formation and nuclear activity in its constituent galaxies and intra-group medium. We associate five dwarf galaxies with the group and update the velocity dispersion, leading to an increase in the dynamical mass of the group of up to a factor of 10 (to 2.8 x 10(exp 13) Stellar Mass), and a subsequent revision of its evolutionary stage. Star formation is proceeding at a level consistent with the morphological types of the four main galaxies, of which two are star-forming and the other two quiescent. Unlike in some other compact groups, star-forming complexes across HCG 59 closely follow mass-radius scaling relations typical of nearby galaxies. In contrast, the ancient globular cluster populations in galaxies HCG 59A and B show intriguing irregularities, and two extragalactic HII regions are found just west of B. We age-date a faint stellar stream in the intra-group medium at approx. 1 Gyr to examine recent interactions. We detect a likely low-luminosity AGN in HCG 59A by its approx. 10(exp 40) erg/s X-ray emission; the active nucleus rather than star formation can account for the UV+IR SED. We discuss the implications of our findings in the context of galaxy evolution in dense environments.

Perturbative Quantum Gauge Theories on Manifolds with Boundary

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Mnev, Pavel; Reshetikhin, Nicolai

2018-01-01

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF theory and its perturbations, including nontopological ones, are presented.
3d Abelian dualities with boundaries

NASA Astrophysics Data System (ADS)

Aitken, Kyle; Baumgartner, Andrew; Karch, Andreas; Robinson, Brandon

2018-03-01

We establish the action of three-dimensional bosonization and particle-vortex duality in the presence of a boundary, which supports a non-anomalous two-dimensional theory. We confirm our prescription using a microscopic realization of the duality in terms of a Euclidean lattice.
Readiness Review of BWXT for Fabrication of AGR 5/6/7 Compacts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marshall, Douglas William; Sharp, Michelle Tracy

In support of preparations for fabricating compacts for the Advanced Gas Reactor (AGR) fuel qualification irradiation experiments (AGR-5/6/7), Idaho National Laboratory (INL) conducted a readiness review of the BWX Technology (BWXT) procedures, processes, and equipment associated with compact fabrication activities at the BWXT Nuclear Operations Group (BWXT-NOG) facility outside Lynchburg, VirginiaVA. The readiness review used quality assurance requirements taken from the American Society of Mechanical Engineers (ASME) Nuclear Quality Assurance Standard (NQA-1-2008/1a-2009) as a basis to assess readiness to start compact fabrication.
Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

NASA Astrophysics Data System (ADS)

Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.

2016-12-01

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.
Investigations into Gravitational Wave Emission from Compact Body Inspiral into Massive Black Holes

NASA Technical Reports Server (NTRS)

Hughes, Scott A.

2005-01-01

In contrast to year 1 (when much of the activity associated with this grant focused upon developing our group at MIT), year 2 was a period of very focused attention on research problems. We made significant progress developing relativistic waveforms for the extreme mass ratio inspiral problem; we have pushed forward a formalism our group developed for mapping the spacetimes of massive compact objects; and, in collaboration with the Caltech group, we began to develop a framework for addressing issues in LISA data analysis for extreme mass ratio systems.
Refined 3d-3d correspondence

NASA Astrophysics Data System (ADS)

Alday, Luis F.; Genolini, Pietro Benetti; Bullimore, Mathew; van Loon, Mark

2017-04-01

We explore aspects of the correspondence between Seifert 3-manifolds and 3d N = 2 supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d N = 2 theories constructed from boundary conditions and interfaces in a 4d N = 2∗ theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d N = 2∗ theory. In the presence of a mass parameter cfor the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the S-matrix of refined Chern-Simons theory.
Building the Hot Intra-Group Medium in Spiral-Rich Compact Groups

NASA Astrophysics Data System (ADS)

O'Sullivan, Ewan

2014-11-01

Galaxy groups provide a natural laboratory for investigating the formation of the hot intergalactic medium (IGM). While galaxy clusters gain most of their hot gas through accretion and gravitational shocks, in groups the processes of galaxy evolution (stripping, collisions, star formation) play an important role in the initial build up of the hot halo. We present Chandra and XMM-Newton observations of groups still in the process of forming their IGM, including the well known compact groups HCG 16 and Stephan's Quintet (HCG 92). We show that starburst winds and shock-heating of stripped HI provide important contributions of gas and metals to the IGM, and discuss the impact of gas stripping, enhanced star formation and nuclear activity in the group member galaxies.
The Koslowski-Sahlmann representation: quantum configuration space

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Varadarajan, Madhavan

2014-09-01

The Koslowski-Sahlmann (KS) representation is a generalization of the representation underlying the discrete spatial geometry of loop quantum gravity (LQG), to accommodate states labelled by smooth spatial geometries. As shown recently, the KS representation supports, in addition to the action of the holonomy and flux operators, the action of operators which are the quantum counterparts of certain connection dependent functions known as ‘background exponentials’. Here we show that the KS representation displays the following properties which are the exact counterparts of LQG ones: (i) the abelian * algebra of SU(2) holonomies and ‘U(1)’ background exponentials can be completed to a C* algebra, (ii) the space of semianalytic SU(2) connections is topologically dense in the spectrum of this algebra, (iii) there exists a measure on this spectrum for which the KS Hilbert space is realized as the space of square integrable functions on the spectrum, (iv) the spectrum admits a characterization as a projective limit of finite numbers of copies of SU(2) and U(1), (v) the algebra underlying the KS representation is constructed from cylindrical functions and their derivations in exactly the same way as the LQG (holonomy-flux) algebra except that the KS cylindrical functions depend on the holonomies and the background exponentials, this extra dependence being responsible for the differences between the KS and LQG algebras. While these results are obtained for compact spaces, they are expected to be of use for the construction of the KS representation in the asymptotically flat case.
Preparation of the femoral bone cavity in cementless stems: broaching versus compaction

PubMed Central

Hjorth, Mette H; Stilling, Maiken; Søballe, Kjeld; Nielsen, Poul Torben; Christensen, Poul H; Kold, Søren

2016-01-01

Background and purpose — Short-term experimental studies have confirmed that there is superior fixation of cementless implants inserted with compaction compared to broaching of the cancellous bone. Patients and methods — 1-stage, bilateral primary THA was performed in 28 patients between May 2001 and September 2007. The patients were randomized to femoral bone preparation with broaching on 1 side and compaction on the other side. 8 patients declined to attend the postoperative follow-up, leaving 20 patients (13 male) with a mean age of 58 (36–70) years for evaluation. The patients were followed with radiostereometric analysis (RSA) at baseline, at 6 and 12 weeks, and at 1, 2, and 5 years, and measurements of periprosthetic bone mineral density (BMD) at baseline and at 1, 2, and 5 years. The subjective part of the Harris hip score (HHS) and details of complications throughout the observation period were obtained at a mean interval of 6.3 (3.0–9.5) years after surgery. Results — Femoral stems in the compaction group had a higher degree of medio-lateral migration (0.21 mm, 95% CI: 0.03–0.40) than femoral stems in the broaching group at 5 years (p = 0.02). No other significant differences in translations or rotations were found between the 2 surgical techniques at 2 years (p > 0.4) and 5 years (p > 0.7) postoperatively. There were no individual stems with continuous migration. Periprosthetic BMD in the 7 Gruen zones was similar at 2 years and at 5 years. Intraoperative femoral fractures occurred in 2 of 20 compacted hips, but there were none in the 20 broached hips. The HHS and dislocations were similar in the 2 groups at 6.3 (3.0–9.5) years after surgery. Interpretation — Bone compaction as a surgical technique with the Bi-Metric stem did not show the superior outcomes expected compared to conventional broaching. Furthermore, 2 periprosthetic fractures occurred using the compaction technique, so we cannot recommend compaction for insertion of the cementless Bi-Metric stem. PMID:27759486
Dimension changing phase transitions in instanton crystals

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Sonnenschein, Jacob

2014-04-01

We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D → 4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions — the 1D lattice of instantons in a harmonic potential V ∝ , and the zigzag-shaped lattice as a first stage of the 1D → 2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M 2 /M 3 /M 4 ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements of a , Klein, prismatic, or dihedral subgroup of the , as well as irrational but link-periodic patterns. For the zigzag-shaped lattices, we detected 4 distinct orientation phases — the anti-ferromagnet, another abelian phase, and two non-abelian phases. Allowing the zigzag amplitude to vary as a function of increasing compression force, we obtained the phase diagrams for the straight and zigzag-shaped lattices in the (force , M 3 /M 4), (chemical potential , M 3 /M 4), and (density , M 3 /M 4) planes. Some of the transitions between these phases are second-order while others are first-order. Our techniques can be applied to other types of non-abelian crystals.
In vitro effectiveness of antimicrobial photodynamic therapy (APDT) using a 660 nm laser and malachite green dye in Staphylococcus aureus biofilms arranged on compact and cancellous bone specimens.

PubMed

Rosa, Luciano Pereira; da Silva, Francine Cristina; Nader, Sumaia Alves; Meira, Giselle Andrade; Viana, Magda Souza

2014-11-01

The aim of this study was to evaluate the in vitro effectiveness of antimicrobial photodynamic therapy (APDT) using a 660 nm visible laser combined with malachite green (MG) dye in the inactivation of Staphylococcus aureus (ATCC 25923) biofilms formed within compact and cancellous bone specimens. Specimens of 80 compact bones and 80 cancellous bones were contaminated with a standard suspension of S. aureus and incubated for 14 days at 37 °C to allow for the formation of biofilms. The specimens were divided into the following groups (n = 10) according to the treatment conditions: PS-L - (control - no treatment), PS+L - (only MG for 5 min), PS-L + 90 (only laser irradiation for 90 s), PS-L + 180 (only laser irradiation for 180 s), PS-L + 300 (only laser irradiation for 300 s), APDT90 (APDT for 90 s), APDT180 (APDT for 180 s), and APDT300 (APDT for 300 s). The findings were statistically analyzed using an ANOVA 5%. All of the experimental groups were significantly different from the control group for both the compact and cancellous bone specimens. The compact bone specimens that received APDT treatment (for either 90, 180, or 300 s) showed reductions in the log10 CFU/ml of S. aureus by a magnitude of 4 log10. Cancellous bone specimens treated with 300 s of APDT showed the highest efficacy, and these specimens had a reduction in S. aureus CFU/ml by a factor of 3 log10. APDT treatment using these proposed parameters in combination with MG was effective at inactivating S. aureus biofilms in compact and cancellous bone specimens.
Effectiveness of antimicrobial photodynamic therapy using a 660 nm laser and methyline blue dye for inactivating Staphylococcus aureus biofilms in compact and cancellous bones: An in vitro study.

PubMed

Rosa, Luciano Pereira; Silva, Francine Cristina da; Nader, Sumaia Alves; Meira, Giselle Andrade; Viana, Magda Souza

2015-06-01

New therapeutic modalities such as antimicrobial photodynamic therapy (APDT) has been investigated in order to be a valid alternative to the treatment of infections caused by different microorganisms. This work evaluated the in vitro effectiveness of Antimicrobial Photodynamic Therapy (APDT) using 660 nm laser combined with methylene blue dye to inactivate Staphylococcus aureus (ATCC 25923) biofilms in compact and cancellous bones specimens. Eighty specimens of compact bone and 80 specimens of cancellous bone were contaminated with a standard suspension of S. aureus and incubated for 14 days at 37°C to induce the formation of biofilms. The specimens were then divided into groups (n = 10) according to the established treatment: PS-L- (control--no treatment), PS+L- (only AM for 5 min in the dark), PS-L+90 (only laser irradiation for 90 s), PS-L+180 (only laser irradiation for 180 s), PS-L+300 (only laser irradiation for 300 s), APDT90 (APDT for 90 s), APDT180 (APDT for 180 s), and APDT300 (APDT for 300 s). The findings were statistically analyzed by ANOVA 5%. All of the experimental treatments showed a significant reduction (log 10 CFU/mL) of S. aureus biofilms in compact and cancellous bones specimens compared with the control group, and the APDT group was the most effective. Compact specimens treated with APDT showed the greatest reduction in biofilms compared with cancellous specimens, regardless of length of treatment. APDT with methylene blue dye and a 660 nm laser proved to be effective in inactivating S. aureus biofilms formed in compact and cancellous bone. Copyright © 2015 Elsevier B.V. All rights reserved.
Elliptic complexes over C∗-algebras of compact operators

NASA Astrophysics Data System (ADS)

Krýsl, Svatopluk

2016-03-01

For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.
Scaling analysis of the non-Abelian quasiparticle tunneling in Z}}_k FQH states

NASA Astrophysics Data System (ADS)

Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang

2018-06-01

Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge–edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read–Rezayi states for and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.
Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit

NASA Astrophysics Data System (ADS)

Danilin, S.; Vepsäläinen, A.; Paraoanu, G. S.

2018-05-01

Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the (∣0〉, ∣2〉) subspace of a three-level (qutrit) transmon device fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creation of arbitrary superpositions in this subspace by changing the amplitudes of the pulses and the relative phase between them. We use two-photon pulses acting in the holonomic subspace to reveal the coherence of the state created by the geometric gate pulses and to prepare different superposition states. We also test the action of holonomic NOT and Hadamard gates on superpositions in the (| 0> ,| 2> ) subspace.
Tsallis’ quantum q-fields

NASA Astrophysics Data System (ADS)

Plastino, A.; Rocca, M. C.

2018-05-01

We generalize several well known quantum equations to a Tsallis’ q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schródinger, q-Klein-Gordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601 (2011), EPL 118, 61004 (2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle. These q-fields are meaningful at very high energies (TeV scale) for q = 1.15, high energies (GeV scale) for q = 1.001, and low energies (MeV scale) for q = 1.000001 [Nucl. Phys. A 955 (2016) 16 and references therein]. (See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields’ logarithms.
Strings, boundary fermions and coincident D-branes

NASA Astrophysics Data System (ADS)

Wulff, Linus

2007-01-01

This thesis describes an attempt to write down covariant actions for coincident D-branes using so-called boundary fermions instead of matrices to describe the non-abelian fields. These fermions can be thought of as Chan-Paton degrees of freedom for the open string. It is shown that by gauge-fixing and by suitably quantizing these boundary fermions the non-abelian action that is known, the Myers action, can be reproduced. Furthermore it is shown that under natural assumptions, unlike the Myers action, the action formulated using boundary fermions also posseses kappa-symmetry when formulated on superspace. Another aspect of string theory discussed in this thesis is that of tensionless strings. These are of great interest for example because of their possible relation to higher spin gauge theories via the AdS/CFT-correspondence. The tensionless superstring in a plane wave background, a Penrose limit of the near-horizon geometry of a stack of D3-branes, is considered and compared to the tensile case.

Gauge and integrable theories in loop spaces

NASA Astrophysics Data System (ADS)

Ferreira, L. A.; Luchini, G.

2012-05-01

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.
Topological transport from a black hole

NASA Astrophysics Data System (ADS)

Melnikov, Dmitry

2018-03-01

In this paper the low temperature zero-frequency transport in a 2 + 1-dimensional theory dual to a dyonic black hole is discussed. It is shown that transport exhibits topological features: the transverse electric and heat conductivities satisfy the Wiedemann-Franz law of free electrons; the direct heat conductivity is measured in units of the central charge of CFT2+1, while the direct electric conductivity vanishes; the thermoelectric conductivity is non-zero at vanishing temperature, while the O (T) behavior, controlled by the Mott relation, is subleading. Provided that the entropy of the black hole, and the dual system, is non-vanishing at T = 0, the observations indicate that the dyonic black hole describes a ħ → 0 limit of a highly degenerate topological state, in which the black hole charge measures the density of excited non-abelian quasiparticles. The holographic description gives further evidence that non-abelian nature of quasiparticles can be determined by the low temperature behavior of the thermoelectric transport.
Edge states at phase boundaries and their stability

NASA Astrophysics Data System (ADS)

Asorey, M.; Balachandran, A. P.; Pérez-Pardo, J. M.

2016-10-01

We analyze the effects of Robin-like boundary conditions on different quantum field theories of spin 0, 1/2 and 1 on manifolds with boundaries. In particular, we show that these conditions often lead to the appearance of edge states. These states play a significant role in physical phenomena like quantum Hall effect and topological insulators. We prove in a rigorous way the existence of spectral lower bounds on the kinetic term of different Hamiltonians, even in the case of Abelian gauge fields where it is a non-elliptic differential operator. This guarantees the stability and consistency of massive field theories with masses larger than the lower bound of the kinetic term. Moreover, we find an upper bound for the deepest edge state. In the case of Abelian gauge theories, we analyze a generalization of Robin boundary conditions. For Dirac fermions, we analyze the cases of Atiyah-Patodi-Singer and chiral bag boundary conditions. The explicit dependence of the bounds on the boundary conditions and the size of the system is derived under general assumptions.
Edge theory approach to topological entanglement entropy, mutual information, and entanglement negativity in Chern-Simons theories

NASA Astrophysics Data System (ADS)

Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei

2016-06-01

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g , which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.
Quantification of cancellous bone-compaction due to DHS Blade insertion and influence upon cut-out resistance.

PubMed

Windolf, Markus; Muths, Raphael; Braunstein, Volker; Gueorguiev, Boyko; Hänni, Markus; Schwieger, Karsten

2009-01-01

Compaction of cancellous bone is believed to prevent cut-out. This in vitro study quantified the compaction in the femoral head due to insertion of a dynamic hip screw-blade with and without predrilling and investigated the resulting implant anchorage under cyclic loading. Eight pairs of human cadaveric femoral heads were instrumented with a dynamic hip screw-blade made of Polyetheretherketon. Pairwise instrumentation was performed either with or without predrilling the specimens. CT scanning was performed before and after implantation, to measure bone-compaction. Subsequently the implant was removed and a third scan was performed to analyze the relaxation of the bone structure. Commercial implants were reinserted and the specimens were cyclically loaded until onset of cut-out occurred. The bone-implant interface was monitored by means of fluoroscopic imaging throughout the experiment. Paired t-tests were performed to identify differences regarding compaction, relaxation and cycles to failure. Bone density in the surrounding of the implant increased about 30% for the non-predrilled and 20% for the predrilled group when inserting the implant. After implant removal the predrilled specimens fully relaxed; the non-predrilled group showed about 10% plastic deformation. No differences were found regarding cycles to failure (P=0.32). Significant bone-compaction due to blade insertion was verified. Even though compaction was lower when predrilling the specimens, mainly elastic deformation was present, which is believed to primarily enhance the implant anchorage. Cyclic loading tests confirmed this thesis. The importance of the implantation technique with regard to predrilling is therefore decreased.
A linearization of quantum channels

NASA Astrophysics Data System (ADS)

Crowder, Tanner

2015-06-01

Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.
The long flow to freedom

DOE PAGES

Aharony, Ofer; Razamat, Shlomo S.; Seiberg, Nathan; ...

2017-02-10

Two-dimensional field theories do not have a moduli space of vacua. Instead, it is common that their low-energy behavior is a sigma model with a target space. When this target space is compact its renormalization group flow is standard. When it is non-compact the continuous spectrum of operators can change the qualitative behavior. Here we discuss two-dimensional gauge theories with N = (2,2) supersymmetry. We focus on two specific theories, for which we argue that they flow to free chiral multiplets at low energies: the U(1) gauge theory with one flavor (two chiral superfields with charges plus and minus one)more » and a non-zero Fayet-Iliopoulos term, and pure SU( N) gauge theories. We argue that the renormalization group flow of these theories has an interesting order of limits issue. Holding the position on the target space fixed, the space flattens out under the renormalization group. On the other hand, if we first go to infinity on the target space and then perform the renormalization group, we always have a non-trivial space, e.g. a cone with a deficit angle. We explain how to interpret low-energy dualities between theories with non-compact target spaces. As a result, we expect a similar qualitative behavior also for other non-compact sigma models, even when they do not flow to free theories.« less
Scaled lattice fermion fields, stability bounds, and regularity

NASA Astrophysics Data System (ADS)

O'Carroll, Michael; Faria da Veiga, Paulo A.

2018-02-01

We consider locally gauge-invariant lattice quantum field theory models with locally scaled Wilson-Fermi fields in d = 1, 2, 3, 4 spacetime dimensions. The use of scaled fermions preserves Osterwalder-Seiler positivity and the spectral content of the models (the decay rates of correlations are unchanged in the infinite lattice). In addition, it also results in less singular, more regular behavior in the continuum limit. Precisely, we treat general fermionic gauge and purely fermionic lattice models in an imaginary-time functional integral formulation. Starting with a hypercubic finite lattice Λ ⊂(aZ ) d, a ∈ (0, 1], and considering the partition function of non-Abelian and Abelian gauge models (the free fermion case is included) neglecting the pure gauge interactions, we obtain stability bounds uniformly in the lattice spacing a ∈ (0, 1]. These bounds imply, at least in the subsequential sense, the existence of the thermodynamic (Λ ↗ (aZ ) d) and the continuum (a ↘ 0) limits. Specializing to the U(1) gauge group, the known non-intersecting loop expansion for the d = 2 partition function is extended to d = 3 and the thermodynamic limit of the free energy is shown to exist with a bound independent of a ∈ (0, 1]. In the case of scaled free Fermi fields (corresponding to a trivial gauge group with only the identity element), spectral representations are obtained for the partition function, free energy, and correlations. The thermodynamic and continuum limits of the free fermion free energy are shown to exist. The thermodynamic limit of n-point correlations also exist with bounds independent of the point locations and a ∈ (0, 1], and with no n! dependence. Also, a time-zero Hilbert-Fock space is constructed, as well as time-zero, spatially pointwise scaled fermion creation operators which are shown to be norm bounded uniformly in a ∈ (0, 1]. The use of our scaled fields since the beginning allows us to extract and isolate the singularities of the free energy when a ↘ 0.
Statistical study of some Lee galaxy groups

NASA Astrophysics Data System (ADS)

Mohamed, Sabry A.; Fouad, Ahmed M.

2017-12-01

Compact groups of galaxies are systems of small number of galaxies close to each other. They are a good laboratory to study galaxy properties, such as structure, morphology and evolution which are affected by the environment and galaxy interactions. We applied the tree clustering technique (the Euclidean separation distance coefficients) to test the physical reality of groups and used certain criteria (Sabry et al., 2009) depending on the physical attributes of the galaxies. The sample of the data is the quintets groups of Lee compact groups of galaxies (Lee et al., 2004). It is based on a modified version of Hickson's criteria (Hickson, 1982). The results reveal the membership of each galaxy and how it is related to its group. The tables of groups and their members are included. Our results indicates that 12 Groups are real groups with real members while 18 Groups have one galaxy that has attribute discordant and should be discarded from its group.
Quantum Engineering of Dynamical Gauge Fields on Optical Lattices

DTIC Science & Technology

2016-07-08

exact blocking formulas from the TRG formulation of the transfer matrix. The second is a worm algorithm. The particle number distributions obtained...a fact that can be explained by an approximate particle- hole symmetry. We have also developed a computer code suite for simulating the Abelian
VLA neutral hydrogen imaging of compact groups of galaxies. II - HCG 31, 44, and 79

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, B.A.; Mcmahon, P.M.; Van gorkom, J.H.

1991-06-01

Neutral hydrogen images of three compact groups of galaxies are presented: HCG 31, 44, and 79. The images were obtained with the very large array (VLA), an on-line Hanning smoothing was applied to the data, and the H I spectral channel was isolated. The images were made on the Pipeline, and were produced by means of a method described by Gorkon and Ekers (1988). The images of HCG 44 are compared with earlier Arecibo observations. The H I emission in HCG 44 is discovered within the galaxies, whereas the emission in 31 and 79 can be found throughout the groupmore » in clouds that are larger than the galaxies. Evidence of a relationship between the compact groups is found in the H I data, and the groups are considered to be merging into a single object. Some of the groups are theorized to be young amorphous galaxies where the H I is still bound to individual galaxies, and which have just begun to condense from the intergalactic medium. The kinematics of the gas are shown to vary, and a common gaseous envelope contains the dwarf galaxies. 42 refs.« less
Dependence of displacement-length scaling relations for fractures and deformation bands on the volumetric changes across them

USGS Publications Warehouse

Schultz, R.A.; Soliva, R.; Fossen, H.; Okubo, C.H.; Reeves, D.M.

2008-01-01

Displacement-length data from faults, joints, veins, igneous dikes, shear deformation bands, and compaction bands define two groups. The first group, having a power-law scaling relation with a slope of n = 1 and therefore a linear dependence of maximum displacement and discontinuity length (Dmax = ??L), comprises faults and shear (non-compactional or non-dilational) deformation bands. These shearing-mode structures, having shearing strains that predominate over volumetric strains across them, grow under conditions of constant driving stress, with the magnitude of near-tip stress on the same order as the rock's yield strength in shear. The second group, having a power-law scaling relation with a slope of n = 0.5 and therefore a dependence of maximum displacement on the square root of discontinuity length (Dmax = ??L0.5), comprises joints, veins, igneous dikes, cataclastic deformation bands, and compaction bands. These opening- and closing-mode structures grow under conditions of constant fracture toughness, implying significant amplification of near-tip stress within a zone of small-scale yielding at the discontinuity tip. Volumetric changes accommodated by grain fragmentation, and thus control of propagation by the rock's fracture toughness, are associated with scaling of predominantly dilational and compactional structures with an exponent of n = 0.5. ?? 2008 Elsevier Ltd.
STELLAR POPULATIONS IN COMPACT GALAXY GROUPS: A MULTI-WAVELENGTH STUDY OF HCGs 16, 22, AND 42, THEIR STAR CLUSTERS, AND DWARF GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.

2013-06-20

We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy. We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to bemore » double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 ''associates'' (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.« less
ENHANCED WARM H{sub 2} EMISSION IN THE COMPACT GROUP MID-INFRARED ''GREEN VALLEY''

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cluver, M. E.; Ogle, P.; Guillard, P.

2013-03-10

We present results from a Spitzer mid-infrared spectroscopy study of a sample of 74 galaxies located in 23 Hickson Compact Groups (HCGs), chosen to be at a dynamically active stage of H I depletion. We find evidence for enhanced warm H{sub 2} emission (i.e., above that associated with UV excitation in star-forming regions) in 14 galaxies ({approx}20%), with 8 galaxies having extreme values of L(H{sub 2} S(0)-S(3))/L(7.7 {mu}m polycyclic aromatic hydrocarbon), in excess of 0.07. Such emission has been seen previously in the compact group HCG 92 (Stephan's Quintet), and was shown to be associated with the dissipation of mechanicalmore » energy associated with a large-scale shock caused when one group member collided, at high velocity, with tidal debris in the intragroup medium. Similarly, shock excitation or turbulent heating is likely responsible for the enhanced H{sub 2} emission in the compact group galaxies, since other sources of heating (UV or X-ray excitation from star formation or active galactic nuclei) are insufficient to account for the observed emission. The group galaxies fall predominantly in a region of mid-infrared color-color space identified by previous studies as being connected to rapid transformations in HCG galaxy evolution. Furthermore, the majority of H{sub 2}-enhanced galaxies lie in the optical ''green valley'' between the blue cloud and red sequence, and are primarily early-type disk systems. We suggest that H{sub 2}-enhanced systems may represent a specific phase in the evolution of galaxies in dense environments and provide new insight into mechanisms which transform galaxies onto the optical red sequence.« less
Stellar Populations in Compact Galaxy Groups: a Multi-wavelength Study of HCGs 16, 22, and 42, Their Star Clusters, and Dwarf Galaxies

NASA Technical Reports Server (NTRS)

Konstantopoulos, I. S.; Maybhate, A.; Charlton, J. C.; Fedotov, K.; Durrell, P. R.; Mulchaey, J. S.; English, J.; Desjardins, T. D.; Gallagher, S. C.; Walker, L. M.;

2013-01-01

We present a multi-wavelength analysis of three compact galaxy groups, Hickson compact groups (HCGs) 16, 22, and 42, which describe a sequence in terms of gas richness, from space- (Swift, Hubble Space Telescope (HST), and Spitzer) and ground-based (Las Campanas Observatory and Cerro Tololo Inter-American Observatory) imaging and spectroscopy.We study various signs of past interactions including a faint, dusty tidal feature about HCG 16A, which we tentatively age-date at <1 Gyr. This represents the possible detection of a tidal feature at the end of its phase of optical observability. Our HST images also resolve what were thought to be double nuclei in HCG 16C and D into multiple, distinct sources, likely to be star clusters. Beyond our phenomenological treatment, we focus primarily on contrasting the stellar populations across these three groups. The star clusters show a remarkable intermediate-age population in HCG 22, and identify the time at which star formation was quenched in HCG 42. We also search for dwarf galaxies at accordant redshifts. The inclusion of 33 members and 27 "associates" (possible members) radically changes group dynamical masses, which in turn may affect previous evolutionary classifications. The extended membership paints a picture of relative isolation in HCGs 16 and 22, but shows HCG 42 to be part of a larger structure, following a dichotomy expected from recent studies. We conclude that (1) star cluster populations provide an excellent metric of evolutionary state, as they can age-date the past epochs of star formation; and (2) the extended dwarf galaxy population must be considered in assessing the dynamical state of a compact group.

Stochastic quantization of topological field theory: Generalized Langevin equation with memory kernel

NASA Astrophysics Data System (ADS)

Menezes, G.; Svaiter, N. F.

2006-07-01

We use the method of stochastic quantization in a topological field theory defined in an Euclidean space, assuming a Langevin equation with a memory kernel. We show that our procedure for the Abelian Chern-Simons theory converges regardless of the nature of the Chern-Simons coefficient.
Symplectic Quantization of a Reducible Theory

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize the Abelian antisymmetric tensor gauge field. It is related to a reducible theory in the sense that all of its constraints are not independent. A procedure like ghost-of-ghost of the BFV method has to be used, but in terms of Lagrange multipliers.
Dual boundary conditions in 3d SCFT's

NASA Astrophysics Data System (ADS)

Dimofte, Tudor; Gaiotto, Davide; Paquette, Natalie M.

2018-05-01

We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d N=2 gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. Examples include basic abelian dualities, level-rank dualities, and Aharony dualities.
Appearance of gauge structure in simple dynamical systems

NASA Technical Reports Server (NTRS)

Wilczek, F.; Zee, A.

1984-01-01

By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.
Plane-parallel waves as duals of the flat background III: T-duality with torsionless B-field

NASA Astrophysics Data System (ADS)

Hlavatý, Ladislav; Petr, Ivo; Petrásek, Filip

2018-04-01

By addition of non-zero, but torsionless B-field, we expand the classification of (non-)Abelian T-duals of the flat background in four dimensions with respect to 1, 2, 3 and 4D subgroups of the Poincaré group. We discuss the influence of the additional B-field on the process of dualization, and identify essential parts of the torsionless B-field that cannot in general be eliminated by coordinate or gauge transformation of the dual background. These effects are demonstrated using particular examples. Due to their physical importance, we focus on duals whose metrics represent plane-parallel (pp-)waves. Besides the previously found metrics, we find new pp-waves depending on parameters originating from the torsionless B-field. These pp-waves are brought into their standard forms in Brinkmann and Rosen coordinates.

Families from supergroups and predictions for leptonic CP violation

NASA Astrophysics Data System (ADS)

Barr, S. M.; Chen, Heng-Yu

2017-10-01

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU( M | N ), can give interesting anomaly-free sets of fermion representations of SU( M ) × SU( N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.
On the symplectic structure of harmonic superspace

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kachkachi, M.; Saidi, E.H.

In this paper, the symplectic properties of harmonic superspace are studied. It is shown that Diff(S[sup 2]) is isomorphic to Diff[sub 0](S[sup 3])/Ab(Diff[sub 0](S[sup 3])), where Diff[sub 0](S[sup 3]) is the group of the diffeomorphisms of S[sup 3] preserving the Cartan charge operator D[sup 0] and Ab(Diff[sub 0](S[sup 3])) is its Abelian subgroup generated by the Cartan vectors L[sub 0] = w[sup 0]D[sup 0]. The authors show also that the eigenvalue equation D[sup 0] [lambda](z) = 0 defines a symplectic structure in harmonic superspace, and the authors calculate the corresponding algebra. The general symplectic invariant coupling of the Maxwell prepotentialmore » is constructed in both flat and curved harmonic superspace. Other features are discussed.« less
Decorated tensor network renormalization for lattice gauge theories and spin foam models

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian

2016-05-01

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
Topologically protected gates for quantum computation with non-Abelian anyons in the Pfaffian quantum Hall state

NASA Astrophysics Data System (ADS)

Georgiev, Lachezar S.

2006-12-01

We extend the topological quantum computation scheme using the Pfaffian quantum Hall state, which has been recently proposed by Das Sarma , in a way that might potentially allow for the topologically protected construction of a universal set of quantum gates. We construct, for the first time, a topologically protected controlled-NOT gate, which is entirely based on quasihole braidings of Pfaffian qubits. All single-qubit gates, except for the π/8 gate, are also explicitly implemented by quasihole braidings. Instead of the π/8 gate we try to construct a topologically protected Toffoli gate, in terms of the controlled-phase gate and CNOT or by a braid-group-based controlled-controlled- Z precursor. We also give a topologically protected realization of the Bravyi-Kitaev two-qubit gate g3 .
A search for extended radio emission from selected compact galaxy groups

NASA Astrophysics Data System (ADS)

Nikiel-Wroczyński, B.; Urbanik, M.; Soida, M.; Beck, R.; Bomans, D. J.

2017-07-01

Context. Studies on compact galaxy groups have led to the conclusion that a plenitude of phenomena take place in between galaxies that form them. However, radio data on these objects are extremely scarce and not much is known concerning the existence and role of the magnetic field in intergalactic space. Aims: We aim to study a small sample of galaxy groups that look promising as possible sources of intergalactic magnetic fields; for example data from radio surveys suggest that most of the radio emission is due to extended, diffuse structures in and out of the galaxies. Methods: We used the Effelsberg 100 m radio telescope at 4.85 GHz and NRAO VLA Sky Survey (NVSS) data at 1.40 GHz. After subtraction of compact sources we analysed the maps searching for diffuse, intergalactic radio emission. Spectral index and magnetic field properties were derived. Results: Intergalactic magnetic fields exist in groups HCG 15 and HCG 60, whereas there are no signs of them in HCG 68. There are also hints of an intergalactic bridge in HCG 44 at 4.85 GHz. Conclusions: Intergalactic magnetic fields exist in galaxy groups and their energy density may be comparable to the thermal (X-ray) density, suggesting an important role of the magnetic field in the intra-group medium, wherever it is detected.
Blockspin renormalization-group study of color confinement due to violation of the non-Abelian Bianchi identity

NASA Astrophysics Data System (ADS)

Suzuki, Tsuneo

2018-02-01

Blockspin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VNABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce (1) smooth gauge fixings such as the maximal center gauge (MCG), (2) blockspin transformations and (3) the tadpole-improved gauge action. The effective action can be determined by adopting the inverse Monte Carlo method. The coupling constants F (i ) of the effective action depend on the coupling of the lattice action β and the number of the blocking step n . But it is found that F (i ) satisfies a beautiful scaling; that is, they are a function of the product b =n a (β ) alone for lattice coupling constants 3.0 ≤β ≤3.9 and the steps of blocking 1 ≤n ≤12 . The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since a →0 as n →∞ for fixed b . The infrared effective monopole action keeps the global color invariance when smooth gauges such as MCG keeping the invariance are adopted. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here as naturally expected from the gauge invariance of the continuum theory. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum, assuming local two-point interactions are dominant as the infrared effective action. The action is formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. When use is made of Berezinskii-Kosterlitz-Thouless (BKT) transformation, the infrared monopole action can be transformed into that of the string model. Since large b =n a (β ) corresponds to the strong-coupling region in the string model, the physical string tension and the lowest glueball mass can be evaluated analytically with the use of the strong-coupling expansion of the string model. The almost perfect action gives us √{σ }≃1.3 √{σphys } for b ≥1.0 (σphys-1 /2) , whereas the scalar glueball mass is kept to be near M (0++)˜3.7 √{σphys } . In addition, using the effective action composed of 10 simple quadratic interactions alone, we can almost explain analytically the scaling function of the squared monopole density determined numerically for a large b region when b >1.2 (σphys-1 /2).
DOE Office of Scientific and Technical Information (OSTI.GOV)

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. Additionally, we conjecture the existence of a new form of the Segal-Bargmann-Hall “coherentmore » state” transform for compact Lie groups G, which we prove for G = U(1){sup n} and support by numerical evidence for G = SU(2). The reason for conjoining this conjecture with the main topic of this article originates in the observation that the coherent state transform can be used as a basic building block of a coherent state quantisation (Berezin quantisation) for compact Lie groups G. But, as Weyl and Berezin quantisation for ℝ{sup 2d} are intimately related by heat kernel evolution, it is natural to ask whether a similar connection exists for compact Lie groups as well. Moreover, since the formulation of space adiabatic perturbation theory requires a (deformation) quantisation as minimal input, we analyse the question to what extent the coherent state quantisation, defined by the Segal-Bargmann-Hall transform, can serve as basis of the former.« less
Representations of the Bondi—Metzner—Sachs group in three space—time dimensions

NASA Astrophysics Data System (ADS)

Melas, Evangelos

2017-01-01

The original Bondi-Metzner-Sachs group B is the common asymptotic symmetry group of all asymptotically at Lorentzian 4-dim space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here, we construct the IRS of B(2, 1), the analogue of B, in 3 space-time dimensions. The IRS are induced from ‘little groups’ which are compact. The finite ‘little groups’ are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2, 1) is not locally compact in the employed Hilbert topology.
Supersymmetric solutions of the cosmological, gauged, ℂ magic model

NASA Astrophysics Data System (ADS)

Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro

2018-05-01

We construct supersymmetric solutions of theories of gauged N = 1 , d = 5 supergravity coupled to vector multiplets with a U(1)R Abelian (Fayet-Iliopoulos) gauging and an independent SU(2) gauging associated to an SU(2) isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU(2) Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the "magic model" based on the Jordan algebra J 3 ℂ with gauge group SU(3) × U(1)R, which is a consistent truncation of maximal SO(6)-gauged supergravity in d = 5 and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual SU(2) instantons, some of which asymptote to AdS5 and some of which are very small, supersymmetric, deformations of AdS5. We also show how some of those solutions can be embedded in Romans' SU(2) × U(1)-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.
Effective data compaction algorithm for vector scan EB writing system

NASA Astrophysics Data System (ADS)

Ueki, Shinichi; Ashida, Isao; Kawahira, Hiroichi

2001-01-01

We have developed a new mask data compaction algorithm dedicated to vector scan electron beam (EB) writing systems for 0.13 μm device generation. Large mask data size has become a significant problem at mask data processing for which data compaction is an important technique. In our new mask data compaction, 'array' representation and 'cell' representation are used. The mask data format for the EB writing system with vector scan supports these representations. The array representation has a pitch and a number of repetitions in both X and Y direction. The cell representation has a definition of figure group and its reference. The new data compaction method has the following three steps. (1) Search arrays of figures by selecting pitches of array so that a number of figures are included. (2) Find out same arrays that have same repetitive pitch and number of figures. (3) Search cells of figures, where the figures in each cell take identical positional relationship. By this new method for the mask data of a 4M-DRAM block gate layer with peripheral circuits, 202 Mbytes without compaction was highly compacted to 6.7 Mbytes in 20 minutes on a 500 MHz PC.
Holonomic quantum computation in the presence of decoherence.

PubMed

Fuentes-Guridi, I; Girelli, F; Livine, E

2005-01-21

We present a scheme to study non-Abelian adiabatic holonomies for open Markovian systems. As an application of our framework, we analyze the robustness of holonomic quantum computation against decoherence. We pinpoint the sources of error that must be corrected to achieve a geometric implementation of quantum computation completely resilient to Markovian decoherence.
Infrared problem in non-Abelian gauge theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yao, Y.

1976-03-22

I extend the Bloch--Nordsieck idea to show that in the lowest nontrivial order of radiative correction the fermion--fermion and gauge-meson--fermion scattering rates are finite, provided that they are averaged over the initial and summed over the final internal spin states. Questions of the physical gauge coupling and infrared slavery are discussed. (AIP)
On Pauli's Invention of Non-Abelian Kaluza-Klein Theory in 1953

NASA Astrophysics Data System (ADS)

Straumann, N.

2002-12-01

There are documents which show that Wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because he saw no way to give masses to the gauge bosons, he refrained from publishing his results formally.
David J. Gross and the Strong Force

Science.gov Websites

allows physicist to predict experimental results to within one part in 100 million. ... The new Nobelists available in electronic documents and on the Web. Documents: Ultraviolet Behavior of Non-Abelian Gauge Gross, Interview (video) Top Some links on this page may take you to non-federal websites. Their
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid

NASA Astrophysics Data System (ADS)

Roy, S. R.; Prasad, A.

1991-07-01

Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Scaling analysis of the non-Abelian quasiparticle tunneling in [Formula: see text] FQH states.

PubMed

Li, Qi; Jiang, Na; Wan, Xin; Hu, Zi-Xiang

2018-06-27

Quasiparticle tunneling between two counter propagating edges through point contacts could provide information on its statistics. Previous study of the short distance tunneling displays a scaling behavior, especially in the conformal limit with zero tunneling distance. The scaling exponents for the non-Abelian quasiparticle tunneling exhibit some non-trivial behaviors. In this work, we revisit the quasiparticle tunneling amplitudes and their scaling behavior in a full range of the tunneling distance by putting the electrons on the surface of a cylinder. The edge-edge distance can be smoothly tuned by varying the aspect ratio for a finite size cylinder. We analyze the scaling behavior of the quasiparticles for the Read-Rezayi [Formula: see text] states for [Formula: see text] and 4 both in the short and long tunneling distance region. The finite size scaling analysis automatically gives us a critical length scale where the anomalous correction appears. We demonstrate this length scale is related to the size of the quasiparticle at which the backscattering between two counter propagating edges starts to be significant.
ADHM and the 4d quantum Hall effect

NASA Astrophysics Data System (ADS)

Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl

2018-04-01

Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.
Probing the holographic principle using dynamical gauge effects from open spin-orbit coupling

NASA Astrophysics Data System (ADS)

Zhao, Jianshi; Price, Craig; Liu, Qi; Gemelke, Nathan

2016-05-01

Dynamical gauge fields result from locally defined symmetries and an effective over-labeling of quantum states. Coupling atoms weakly to a reservoir of laser modes can create an effective dynamical gauge field purely due to the disregard of information in the optical states. Here we report measurements revealing effects of open spin-orbit coupling in a system where an effective model can be formed from a non-abelian SU(2) × U(1) field theory following the Yang-Mills construct. Forming a close analogy to dynamical gauge effects in quantum chromodynamics, we extract a measure of atomic motion which reveals the analog of a closing mass gap for the relevant gauge boson, shedding insight on long standing open problems in gauge-fixing scale anomalies. Using arguments following the holographic principle, we measure scaling relations which can be understood by quantifying information present in the local potential. New prospects using these techniques for developing fractionalization of multi-particle and macroscopic systems using dissipative and non-abelian gauge fields will also be discussed. We acknowledge support from NSF Award No. 1068570, and the Charles E. Kaufman Foundation.
Fast non-Abelian geometric gates via transitionless quantum driving.

PubMed

Zhang, J; Kyaw, Thi Ha; Tong, D M; Sjöqvist, Erik; Kwek, Leong-Chuan

2015-12-21

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
Fast non-Abelian geometric gates via transitionless quantum driving

PubMed Central

Zhang, J.; Kyaw, Thi Ha; Tong, D. M.; Sjöqvist, Erik; Kwek, Leong-Chuan

2015-01-01

A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer. PMID:26687580

Paired quantum Hall states on noncommutative two-tori

NASA Astrophysics Data System (ADS)

Marotta, Vincenzo; Naddeo, Adele

2010-08-01

By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter θ (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings ν=mp/m+2 Cristofano et al. (2000) [1], recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) [2] for the Jain series ν=>m2p/m+1. The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.
New prospects in fixed target searches for dark forces with the SeaQuest experiment at Fermilab

DOE PAGES

Gardner, S.; Holt, R. J.; Tadepalli, A. S.

2016-06-10

An intense 120 GeV proton beam incident on an extremely long iron target generates enormous numbers of light-mass particles that also decay within that target. If one of these particles decays to a final state with a hidden gauge boson, or if such a particle is produced as a result of the initial collision, then that weakly interacting hidden-sector particle may traverse the remainder of the target and be detected downstream through its possible decay to an e +e –, μ +μ –, or π +π – final state. These conditions can be realized through an extension of the SeaQuestmore » experiment at Fermilab, and in this initial investigation we consider how it can serve as an ultrasensitive probe of hidden vector gauge forces, both Abelian and non-Abelian. Here a light, weakly coupled hidden sector may well explain the dark matter established through astrophysical observations, and the proposed search can provide tangible evidence for its existence—or, alternatively, constrain a “sea” of possibilities.« less
Geometric construction of quantum hall clustering Hamiltonians

DOE PAGES

Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

2015-10-08

In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicatedmore » many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less
A noncompact Weyl-Einstein-Yang-Mills model: A semiclassical quantum gravity

NASA Astrophysics Data System (ADS)

Dengiz, Suat

2017-08-01

We construct and study perturbative unitarity (i.e., ghost and tachyon analysis) of a 3 + 1-dimensional noncompact Weyl-Einstein-Yang-Mills model. The model describes a local noncompact Weyl's scale plus SU(N) phase invariant Higgs-like field,conformally coupled to a generic Weyl-invariant dynamical background. Here, the Higgs-like sector generates the Weyl's conformal invariance of system. The action does not admit any dimensionful parameter and genuine presence of de Sitter vacuum spontaneously breaks the noncompact gauge symmetry in an analogous manner to the Standard Model Higgs mechanism. As to flat spacetime, the dimensionful parameter is generated within the dimensional transmutation in quantum field theories, and thus the symmetry is radiatively broken through the one-loop Effective Coleman-Weinberg potential. We show that the mere expectation of reducing to Einstein's gravity in the broken phases forbids anti-de Sitter space to be its stable vacua. The model is unitary in de Sitter and flat vacua around which a massless graviton, N2 - 1 massless scalar bosons, N massless Dirac fermions, N2 - 1 Proca-type massive Abelian and non-Abelian vector bosons are generically propagated.
MID-INFRARED EVIDENCE FOR ACCELERATED EVOLUTION IN COMPACT GROUP GALAXIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walker, Lisa May; Johnson, Kelsey E.; Gallagher, Sarah C.

2010-11-15

Compact galaxy groups are at the extremes of the group environment, with high number densities and low velocity dispersions that likely affect member galaxy evolution. To explore the impact of this environment in detail, we examine the distribution in the mid-infrared (MIR) 3.6-8.0 {mu}m color space of 42 galaxies from 12 Hickson compact groups (HCGs) in comparison with several control samples, including the LVL+SINGS galaxies, interacting galaxies, and galaxies from the Coma Cluster. We find that the HCG galaxies are strongly bimodal, with statistically significant evidence for a gap in their distribution. In contrast, none of the other samples showmore » such a marked gap, and only galaxies in the Coma infall region have a distribution that is statistically consistent with the HCGs in this parameter space. To further investigate the cause of the HCG gap, we compare the galaxy morphologies of the HCG and LVL+SINGS galaxies, and also probe the specific star formation rate (SSFR) of the HCG galaxies. While galaxy morphology in HCG galaxies is strongly linked to position with MIR color space, the more fundamental property appears to be the SSFR, or star formation rate normalized by stellar mass. We conclude that the unusual MIR color distribution of HCG galaxies is a direct product of their environment, which is most similar to that of the Coma infall region. In both cases, galaxy densities are high, but gas has not been fully processed or stripped. We speculate that the compact group environment fosters accelerated evolution of galaxies from star-forming and neutral gas-rich to quiescent and neutral gas-poor, leaving few members in the MIR gap at any time.« less
Galaxy interactions in compact groups - II. Abundance and kinematic anomalies in HCG 91c

NASA Astrophysics Data System (ADS)

Vogt, Frédéric P. A.; Dopita, Michael A.; Borthakur, Sanchayeeta; Verdes-Montenegro, Lourdes; Heckman, Timothy M.; Yun, Min S.; Chambers, Kenneth C.

2015-07-01

Galaxies in Hickson Compact Group 91 (HCG 91) were observed with the WiFeS integral field spectrograph as part of our ongoing campaign targeting the ionized gas physics and kinematics inside star-forming members of compact groups. Here, we report the discovery of H II regions with abundance and kinematic offsets in the otherwise unremarkable star-forming spiral HCG 91c. The optical emission line analysis of this galaxy reveals that at least three H II regions harbour an oxygen abundance ˜0.15 dex lower than expected from their immediate surroundings and from the abundance gradient present in the inner regions of HCG 91c. The same star-forming regions are also associated with a small kinematic offset in the form of a lag of 5-10 km s-1 with respect to the local circular rotation of the gas. H I observations of HCG 91 from the Very Large Array and broad-band optical images from Pan-STARRS (Panoramic Survey Telescope And Rapid Response System) suggest that HCG 91c is caught early in its interaction with the other members of HCG 91. We discuss different scenarios to explain the origin of the peculiar star-forming regions detected with WiFeS, and show that evidence points towards infalling and collapsing extraplanar gas clouds at the disc-halo interface, possibly as a consequence of long-range gravitational perturbations of HCG 91c from the other group members. As such, HCG 91c provides evidence that some of the perturbations possibly associated with the early phase of galaxy evolution in compact groups impact the star-forming disc locally, and on sub-kpc scales.
Alternative schemes of predicting lepton mixing parameters from discrete flavor and C P symmetry

NASA Astrophysics Data System (ADS)

Lu, Jun-Nan; Ding, Gui-Jun

2017-01-01

We suggest two alternative schemes to predict lepton mixing angles as well as C P violating phases from a discrete flavor symmetry group combined with C P symmetry. In the first scenario, the flavor and C P symmetry is broken to the residual groups of the structure Z2×C P in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters θν and θl. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant C P transformation, all lepton mixing parameters are determined in terms of three free parameters θ1 ,2 ,3. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters θν ,l and θ1 ,2 ,3 is taken into account. We have studied the lepton mixing patterns arising from the flavor group S4 and C P symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.
The effect of using an inverted master cone in a lateral compaction technique on the density of the gutta-percha fill.

PubMed

Wu, Min-Kai; de Groot, Sjoerd D; van der Sluis, Luc W M; Wesselink, Paul R

2003-09-01

We sought to measure and calculate the percentage of the gutta-percha-filled area in the apical root canal after the use of a standardized or inverted master cone in cold lateral compaction.Study design Two groups of extracted mandibular premolars with a single canal were instrumented with instruments of the same size; furthermore, they were obturated with laterally compacted gutta-percha cones with AH26 used as a sealer. In the first group, a standardized master cone was used with its narrow end in an apical position, whereas in the other group, an inverted master cone was used with its wide end in an apical position. The 2 master cones had the same apical diameter and fit in the apical canal. After lateral compaction, horizontal sections were cut at a level 3 and 5 mm from the apex of each filled tooth. Photographs of the sections were taken by using a microscope equipped with a digital camera; the photos were then scanned as tagged-image file format images. The cross-sectional area of the canal and the gutta-percha were measured by using an image-analysis program. The percentage of gutta-percha-filled area was calculated. At both levels, the inverted master cone produced a significantly higher percentage, statistically, of gutta-percha-filled area than did the standardized master cone (P =.001 at 3 mm; P =.012 at 5 mm). The use of an inverted master cone in cold lateral compaction may facilitate the apical placement of accessory cones, significantly increasing the volume of gutta-percha while reducing the volume of sealer in the apical root canal.
Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications

NASA Astrophysics Data System (ADS)

Martins, M. J.; Melo, C. S.

2009-10-01

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.
Regional Thicknesses and Thickening of Compacted and Trabeculated Myocardial Layers of the Normal Left Ventricle Studied by Cardiovascular Magnetic Resonance

PubMed Central

Dawson, Dana K.; Maceira, Alicia M.; Raj, Vimal J.; Graham, Catriona; Pennell, Dudley J.; Kilner, Philip J.

2011-01-01

Background We used cardiovascular magnetic resonance (CMR) to study normal left ventricular (LV) trabeculation as a basis for differentiation from pathological noncompaction. Methods and Results The apparent end-diastolic (ED) and end-systolic (ES) thicknesses and thickening of trabeculated and compacted myocardial layers were measured in 120 volunteers using a consistent selection of basal, mid, and apical CMR short-axis slices. All had a visible trabeculated layer in 1 or more segments. The compacted but not the trabeculated layer was thicker in men than in women (P<0.01 at ED and ES). When plotted against age, the trabeculated and compacted layer thicknesses demonstrated opposite changes: an increase of the compact layer after the fourth decade at both ED and ES (P<0.05) but a decrease of the trabeculated layer. There was age-related preservation of total wall thickness at ED but an increase at ES (P<0.05). The compacted layer thickened, whereas the trabeculated layer thinned with systole, but neither change differed between sexes. With age, the most trabeculated LV segments showed significantly greater systolic thinning of trabeculated layers and, conversely, greater thickening of the compact segments (P<0.05). Total wall thickening is neither sex nor age dependent. There were no sex differences in the trabeculated/compacted ratio at ES or ED, but the ES trabeculated/compacted ratio was smaller in older (50 to 79 years) versus younger (20 to 49 years) groups (P<0.05). Conclusions We demonstrated age- and sex-related morphometric differences in the apparent trabeculated and compacted layer thicknesses and systolic thinning of the visible trabeculated layer that contrasts with compacted myocardial wall thickening. PMID:21193690
[Study on physical properties of titanium alloy sample fabricated with vacuum-sintered powder metallurgy].

PubMed

Ding, X; Liang, X; Chao, Y; Han, X

2000-06-01

To investigate the physical properties of titanium alloy fabricated with vacuum-sintered powder metallurgy. The titanium powders of three different particle sizes(-160mesh, -200 - +300mesh, -300mesh) were selected, and mixed with copper and aluminum powder in different proportions. Two other groups were made up of titanium powder(-200 - +300mesh) plated with copper and tin. The build-up and, condensation method and a double-direction press with a metal mold were used. The green compacts were sintered at 1000 degrees C for 15 minutes in a vacuum furnace at 0.025 Pa. In the double-direction press, the specimens were compacted at the pressure of 100 MPa, 200 MPa and 300 MPa respectively. Then the linear shrinkage ratio and the opening porosity of the sintered compacts were evaluated respectively. 1. The linear shrinkage ratio of specimens decreased with the increased compacted pressure(P < 0.05). There was no significant difference among the linear shrinkage ratios of three different titanium powders at the same compacted pressure(P > 0.05), but that of titanium powder plated with copper and tin was higher than those of other specimens without plating(P < 0.05). 2. The opening porosity of specimens decreased with the increased compacted pressure(P < 0.05). Three different sized particle of titanium powder did not affect the opening porosity at the same compacted pressure(P > 0.05). The composition of titanium-based metal powder mixtures and the compacted pressures affect the physical properties of sintered compacts. Titanium powder plated with copper and tin is compacted and sintered easily, and the physical properties of sintered compacts are greatly improved.
Chern-Simons Term: Theory and Applications.

NASA Astrophysics Data System (ADS)

Gupta, Kumar Sankar

1992-01-01

We investigate the quantization and applications of Chern-Simons theories to several systems of interest. Elementary canonical methods are employed for the quantization of abelian and nonabelian Chern-Simons actions using ideas from gauge theories and quantum gravity. When the spatial slice is a disc, it yields quantum states at the edge of the disc carrying a representation of the Kac-Moody algebra. We next include sources in this model and their quantum states are shown to be those of a conformal family. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. The spin-statistics theorem is established for Chern-Simons dynamics using purely geometrical techniques. Chern-Simons action is associated with exotic spin and statistics in 2 + 1 dimensions. We study several systems in which the Chern-Simons action affects the spin and statistics. The first class of systems we study consist of G/H models. The solitons of these models are shown to obey anyonic statistics in the presence of a Chern-Simons term. The second system deals with the effect of the Chern -Simons term in a model for high temperature superconductivity. The coefficient of the Chern-Simons term is shown to be quantized, one of its possible values giving fermionic statistics to the solitons of this model. Finally, we study a system of spinning particles interacting with 2 + 1 gravity, the latter being described by an ISO(2,1) Chern-Simons term. An effective action for the particles is obtained by integrating out the gauge fields. Next we construct operators which exchange the particles. They are shown to satisfy the braid relations. There are ambiguities in the quantization of this system which can be exploited to give anyonic statistics to the particles. We also point out that at the level of the first quantized theory, the usual spin-statistics relation need not apply to these particles.
Dark matter cosmic string in the gravitational field of a black hole

NASA Astrophysics Data System (ADS)

Nakonieczny, Łukasz; Nakonieczna, Anna; Rogatko, Marek

2018-03-01

We examined analytically and proposed a numerical model of an Abelian Higgs dark matter vortex in the spacetime of a stationary axisymmetric Kerr black hole. In analytical calculations the dark matter sector was modeled by an addition of a U(1)-gauge field coupled to the visible sector. The backreaction analysis revealed that the impact of the dark vortex presence is far more complicated than causing only a deficit angle. The vortex causes an ergosphere shift and the event horizon velocity is also influenced by its presence. These phenomena are more significant than in the case of a visible vortex sector. The area of the event horizon of a black hole is diminished and this decline is larger in comparison to the Kerr black hole with an Abelian Higgs vortex case. After analyzing the gravitational properties for the general setup, we focused on the subset of models that are motivated by particle physics. We retained the Abelian Higgs model as a description of the dark matter sector (this sector contained a heavy dark photon and an additional complex scalar) and added a real scalar representing the real component of the Higgs doublet in the unitary gauge, as well as an additional U(1)-gauge field representing an ordinary electromagnetic field. Moreover, we considered two coupling channels between the visible and dark sectors, which were the kinetic mixing between the gauge fields and a quartic coupling between the scalar fields. After solving the equations of motion for the matter fields numerically we analyzed properties of the cosmic string in the dark matter sector and its influence on the visible sector fields that are directly coupled to it. We found out that the presence of the cosmic string induced spatial variation in the vacuum expectation value of the Higgs field and a nonzero electromagnetic field around the black hole.
Quasiparticle Tunneling in the Fractional Quantum Hall effect at filling fraction ν=5/2

NASA Astrophysics Data System (ADS)

Radu, Iuliana P.

2009-03-01

In a two-dimensional electron gas (2DEG), in the fractional quantum Hall regime, the quasiparticles are predicted to have fractional charge and statistics, as well as modified Coulomb interactions. The state at filling fraction ν=5/2 is predicted by some theories to have non-abelian statistics, a property that might be exploited for topological quantum computing. However, alternative models with abelian properties have been proposed as well. Weak quasiparticle tunneling between counter-propagating edges is one of the methods that can be used to learn about the properties of the state and potentially distinguish between models describing it. We employ an electrostatically defined quantum point contact (QPC) fabricated on a high mobility GaAs/AlGaAs 2DEG to create a constriction where quasiparticles can tunnel between counter-propagating edges. We study the temperature and dc bias dependence of the tunneling conductance, while preserving the same filling fraction in the constriction and the bulk of the sample. The data show scaling of the bias-dependent tunneling over a range of temperatures, in agreement with the theory of weak quasiparticle tunneling, and we extract values for the effective charge and interaction parameter of the quasiparticles. The ranges of values obtained are consistent with those predicted by certain models describing the 5/2 state, indicating as more probable a non-abelian state. This work was done in collaboration with J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer and K. W. West. This work was supported in part by the Army Research Office (W911NF-05-1-0062), the Nanoscale Science and Engineering Center program of NSF (PHY-0117795), NSF (DMR-0701386), the Center for Materials Science and Engineering program of NSF (DMR-0213282) at MIT, the Microsoft Corporation Project Q, and the Center for Nanoscale Systems at Harvard University.
Orbifold E-functions of dual invertible polynomials

NASA Astrophysics Data System (ADS)

Ebeling, Wolfgang; Gusein-Zade, Sabir M.; Takahashi, Atsushi

2016-08-01

An invertible polynomial is a weighted homogeneous polynomial with the number of monomials coinciding with the number of variables and such that the weights of the variables and the quasi-degree are well defined. In the framework of the search for mirror symmetric orbifold Landau-Ginzburg models, P. Berglund and M. Henningson considered a pair (f , G) consisting of an invertible polynomial f and an abelian group G of its symmetries together with a dual pair (f ˜ , G ˜) . We consider the so-called orbifold E-function of such a pair (f , G) which is a generating function for the exponents of the monodromy action on an orbifold version of the mixed Hodge structure on the Milnor fibre of f. We prove that the orbifold E-functions of Berglund-Henningson dual pairs coincide up to a sign depending on the number of variables and a simple change of variables. The proof is based on a relation between monomials (say, elements of a monomial basis of the Milnor algebra of an invertible polynomial) and elements of the whole symmetry group of the dual polynomial.
Patterns of symmetry breaking in chiral QCD

NASA Astrophysics Data System (ADS)

Bolognesi, Stefano; Konishi, Kenichi; Shifman, Mikhail

2018-05-01

We consider S U (N ) Yang-Mills theory with massless chiral fermions in a complex representation of the gauge group. The main emphasis is on the so-called hybrid ψ χ η model. The possible patterns of realization of the continuous chiral flavor symmetry are discussed. We argue that the chiral symmetry is broken in conjunction with a dynamical Higgsing of the gauge group (complete or partial) by bifermion condensates. As a result a color-flavor locked symmetry is preserved. The 't Hooft anomaly matching proceeds via saturation of triangles by massless composite fermions or, in a mixed mode, i.e. also by the "weakly" coupled fermions associated with dynamical Abelianization, supplemented by a number of Nambu-Goldstone mesons. Gauge-singlet condensates are of the multifermion type and, though it cannot be excluded, the chiral symmetry realization via such gauge invariant condensates is more contrived (requires a number of four-fermion condensates simultaneously and, even so, problems remain) and less plausible. We conclude that in the model at hand, chiral flavor symmetry implies dynamical Higgsing by bifermion condensates.
Towards a phase diagram for spin foams

NASA Astrophysics Data System (ADS)

Delcamp, Clement; Dittrich, Bianca

2017-11-01

One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin foams. This scheme is based on the concept of decorated tensor networks, which have been introduced recently. Here we develop an algorithm applicable to gauge theories with non-Abelian groups, which for the first time allows for the application of tensor network coarse-graining techniques to proper spin foams. The procedure deals efficiently with the large redundancy of degrees of freedom resulting from gauge invariance. The algorithm is applied to 3D spin foams defined on a cubical lattice which, in contrast to a proper triangulation, allows for non-trivial simplicity constraints. This mimics the construction of spin foams for 4D gravity. For lattice gauge models based on a finite group we use the algorithm to obtain phase diagrams, encoding the continuum limit of a wide range of these models. We find phase transitions for various families of models carrying non-trivial simplicity constraints.
Neutrino mixing in SO(10) GUTs with a non-Abelian flavor symmetry in the hidden sector

NASA Astrophysics Data System (ADS)

Smirnov, Alexei Yu.; Xu, Xun-Jie

2018-05-01

The relation between the mixing matrices of leptons and quarks, UPMNS≈VCKM†U0 , where U0 is a matrix of special forms [e.g., bimaximal (BM) and tribimaximal], can be a clue for understanding the lepton mixing and neutrino masses. It may imply the grand unification and the existence of a hidden sector with certain symmetry that generates U0 and leads to the smallness of neutrino masses. We apply the residual symmetry approach to obtain U0. The residual symmetries of both the visible and hidden sectors are Z2×Z2 . Their embedding in a unified flavor group is considered. We find that there are only several possible structures of U0, including the BM mixing and matrices with elements determined by the golden ratio. Realization of the BM scenario based on the SO(10) grand unified theory with the S4 flavor group is presented. Generic features of this scenario are discussed, in particular, the prediction of C P phase 14 4 ° ≲δCP≲21 0 ° in the minimal version.
Black holes with su(N) gauge field hair and superconducting horizons

NASA Astrophysics Data System (ADS)

Shepherd, Ben L.; Winstanley, Elizabeth

2017-01-01

We present new planar dyonic black hole solutions of the su(N) Einstein-Yang-Mills equations in asymptotically anti-de Sitter space-time, focussing on su(2) and su(3) gauge groups. The magnetic part of the gauge field forms a condensate close to the planar event horizon. We compare the free energy of a non-Abelian hairy black hole with that of an embedded Reissner-Nordström-anti-de Sitter (RN-AdS) black hole having the same Hawking temperature and electric charge. We find that the hairy black holes have lower free energy. We present evidence that there is a phase transition at a critical temperature, above which the only solutions are embedded RN-AdS black holes. At the critical temperature, an RN-AdS black hole can decay into a hairy black hole, and it is thermodynamically favourable to do so. Working in the probe limit, we compute the frequency-dependent conductivity, and find that enlarging the gauge group from su(2) to su(3) eliminates a divergence in the conductivity at nonzero frequency.
Use of the Heimlich valve in a compact autotransfusion device.

PubMed

Schweitzer, E J; Hauer, J M; Swan, K G; Bresch, J R; Harmon, J W; Graeber, G M

1987-05-01

A compact device which evacuates blood from a hemothorax and facilitates rapid autotransfusion was evaluated in dogs. Experimental hemothorax was established surgically by incising the internal mammary artery through a thoracotomy with the animals under general anesthesia. Postoperatively the blood was drained by one of two methods. In the Heimlich valve group (n = 5), blood was drained by a chest tube through a one-way flutter valve into a collapsible plastic bag. In the Sorenson group (n = 5), blood was drained by a chest tube into the Sorenson Autotransfusion System. Blood from these two groups was then autotransfused. In the control group (n = 5), the drained blood was not autotransfused. Results showed no statistical difference between the two autotransfusion groups in the volume of blood collected, circulating fibrinogen levels, platelet counts, stroma-free hemoglobin levels, prothrombin time, or 51Cr-labeled RBC survival. There was a significant drop in the circulating platelet count, which returned to normal by 24 hours, in both groups of dogs which were autotransfused. We conclude that autotransfusion of blood collected by a compact device which utilizes a Heimlich valve and requires no suction is similar to using the Sorenson Autotransfusion System. It may be safe to use the Heimlich valve to collect blood for autotransfusion in clinical situations, where its qualities of simplicity, portability and a minimum requirement for storage space are desirable.

VLA observations of hydrogen in HCG 18

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, B.A.; Van gorkom, J.H.

1988-02-01

Images are presented of the neutral hydrogen (H I) in the direction of the compact group of galaxies HCG 18. This H I emission is identified with a single cloud, centered on the galaxies b, c, and d and smoothly distributed over a region twice the size of the compact group. The cloud appears to be in regular rotation with a period no longer than 8 x 10 to the 8th yr. The systematic velocity of the gas lies within 1 sigma of the mean velocity of the group; however, the cloud is not clearly associated with any particular galaxy,more » but surrounds all three, which may be one irregular galaxy. 17 references.« less
Continuous Advances in QCD 2008

NASA Astrophysics Data System (ADS)

Peloso, Marco M.

2008-12-01

1. High-order calculations in QCD and in general gauge theories. NLO evolution of color dipoles / I. Balitsky. Recent perturbative results on heavy quark decays / J. H. Piclum, M. Dowling, A. Pak. Leading and non-leading singularities in gauge theory hard scattering / G. Sterman. The space-cone gauge, Lorentz invariance and on-shell recursion for one-loop Yang-Mills amplitudes / D. Vaman, Y.-P. Yao -- 2. Heavy flavor physics. Exotic cc¯ mesons / E. Braaten. Search for new physics in B[symbol]-mixing / A. J. Lenz. Implications of D[symbol]-D[symbol] mixing for new physics / A. A. Petrov. Precise determinations of the charm quark mass / M. Steinhauser -- 3. Quark-gluon dynamics at high density and/or high temperature. Crystalline condensate in the chiral Gross-Neveu model / G. V. Dunne, G. Basar. The strong coupling constant at low and high energies / J. H. Kühn. Quarkyonic matter and the phase diagram of QCD / L. McLerran. Statistical QCD with non-positive measure / J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot. From equilibrium to transport properties of strongly correlated fermi liquids / T. Schäfer. Lessons from random matrix theory for QCD at finite density / K. Splittorff, J. J. M. Verbaarschot -- 4. Methods and models of holographic correspondence. Soft-wall dynamics in AdS/QCD / B. Batell. Holographic QCD / N. Evans, E. Threlfall. QCD glueball sum rules and vacuum topology / H. Forkel. The pion form factor in AdS/QCD / H. J. Kwee, R. F. Lebed. The fast life of holographic mesons / R. C. Myers, A. Sinha. Properties of Baryons from D-branes and instantons / S. Sugimoto. The master space of N = 1 quiver gauge theories: counting BPS operators / A. Zaffaroni. Topological field congurations. Skyrmions in theories with massless adjoint quarks / R. Auzzi. Domain walls, localization and confinement: what binds strings inside walls / S. Bolognesi. Static interactions of non-abelian vortices / M. Eto. Vortices which do not abelianize dynamically: semi-classical origin of non-abelian monopoles / K. Konishi. A generalized construction for lumps and non-abelian vortices / W. Vinci -- 6. Dynamics in supersymmetric theories. Cusp anomalous dimension in planar maximally supersymmetric Yang-Mills theory / B. Basso. SO(2M) and USp(2M) (hyper)Kähler quotients and lumps / S. B. Gudnason -- 7. Other developments. Gluinos condensing at the CCNI: 4096 CPUs weigh in / J. Giedt ... [et al.]. Baryon Regge trajectories and the 1/N[symbol] expansion / J. L. Goity, N. Matagne. Infrared behavior of the fermion propagator in unquenched QED[symbol] with finite threshold effects / Y. Hoshino. Gauge fields in accelerated frames / F. Lenz. QCD at complex coupling, large order in perturbation theory and the gluon condensate / Y. Meurice. 511 KeV line and other diffuse emissions as a trace of the dark matter / A. R. Zhitnitsky -- 8. Glimpses of the conference.
Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

NASA Astrophysics Data System (ADS)

Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd; Thompson, Daniel C.

2017-09-01

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associ-ated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.
Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization

NASA Astrophysics Data System (ADS)

Nedelko, Sergei N.; Voronin, Vladimir V.

2017-03-01

An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(Nf) × SUR(Nf) and UA(1) symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal n-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.
Semiclassics, Goldstone bosons and CFT data

NASA Astrophysics Data System (ADS)

Monin, A.; Pirtskhalava, D.; Rattazzi, R.; Seibold, F. K.

2017-06-01

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.
Supersymmetric tools in Yang-Mills theories at strong coupling: The beginning of a long journey

NASA Astrophysics Data System (ADS)

Shifman, Mikhail

2018-04-01

Development of holomorphy-based methods in super-Yang-Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg’s duality and the Seiberg-Witten solution of 𝒩 = 2 Yang-Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degrees of supersymmetry, supported in some four-dimensional Yang-Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk 𝒩 = 2 theory with the U(2) gauge group and four flavors, which can become critical in a certain limit. This is the case of a “reverse holography,” with a very transparent physical meaning.
Entropy production of doubly stochastic quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Müller-Hermes, Alexander, E-mail: muellerh@posteo.net; Department of Mathematical Sciences, University of Copenhagen, 2100 Copenhagen; Stilck França, Daniel, E-mail: dsfranca@mytum.de

2016-02-15

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an applicationmore » we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.« less
From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
Synthesis of InSb Nanowire Architectures - Building Blocks for Majorana Devices

NASA Astrophysics Data System (ADS)

Car, Diana

Breakthroughs in material development are playing a major role in the emerging field of topological quantum computation with Majorana Zero Modes (MZMs). Due to the strong spin-orbit interaction and large Landé g-factor InSb nanowires are one of the most promising one dimensional material systems in which to detect MZMs. The next generation of Majorana experiments should move beyond zero-mode detection and demonstrate the non-Abelian nature of MZMs by braiding. To achieve this goal advanced material platforms are needed: low-disorder, single-crystalline, planar networks of nanowires with high spin-orbit energy. In this talk I will discuss the formation and electronic properties of InSb nanowire networks. The bottom-up synthesis method we have developed is generic and can be employed to synthesize interconnected nanowire architectures of group III-V, II-VI and IV materials as long as they grow along a <111>direction.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

Two Senate bills, S. 1517 and S. 1578, were the subject of joint hearings on the issue of the disposal of low-level wastes. At issue was the inability to meet the January 1 deadline for the states to develop regional compacts. Witnesses discussed interim measures until the compacts are in place as proposed in the two bills. S. 1517 continues DOE financial and technical assistance, and revises the guidelines for regional compacts. S. 1578 focuses on improving the procedures for establishing and implementing the compacts. The witnesses presented the views of several states, the nuclear and electric power industries, environmentalmore » and safety groups, and others. Two appendices with additional responses and material submitted for the record follow the text of the two bills and the statements and testimony of 24 witnesses.« less
Free Fermions and the Classical Compact Groups

NASA Astrophysics Data System (ADS)

Cunden, Fabio Deelan; Mezzadri, Francesco; O'Connell, Neil

2018-06-01

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.
Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

NASA Astrophysics Data System (ADS)

Gußmann, Alexander

2017-03-01

The existence of the classical black hole solutions of the Einstein-Yang-Mills-Higgs equations with non-Abelian Yang-Mills-Higgs hair implies that not all classical stationary magnetically charged black holes can be uniquely described by their asymptotic characteristics. In fact, in a certain domain of parameters, there exist different spherically-symmetric, non-rotating and asymptotically-flat classical black hole solutions of the Einstein-Yang-Mills-Higgs equations which have the same ADM mass and the same magnetic charge but significantly different geometries in the near-horizon regions. (These are black hole solutions which are described by a Reissner-Nordström metric on the one hand and the black hole solutions with non-Abelian Yang-Mills-Higgs hair which are described by a metric which is not of Reissner-Nordström form on the other hand). One can experimentally distinguish such black holes with the same asymptotic characteristics but different near-horizon geometries classically by probing the near-horizon regions of the black holes. We argue that one way to probe the near-horizon region of a black hole which allows one to distinguish magnetically charged black holes with the same asymptotic characteristics but different near-horizon geometries is by classical scattering of waves. Using the example of a minimally-coupled massless probe scalar field scattered by magnetically charged black holes which can be obtained as solutions of the Einstein-Yang-Mills-Higgs equations with a Higgs triplet and gauge group SU(2) in the limit of an infinite Higgs self-coupling constant we show how, in this case, the scattering cross sections differ for the magnetically charged black holes with different near-horizon geometries but the same asymptotic characteristics. We find in particular that the characteristic glory peaks in the cross sections are located at different scattering angles.
Coherent States for Kronecker Products of Non Compact Groups: Formulation and Applications

NASA Technical Reports Server (NTRS)

Bambah, Bindu A.; Agarwal, Girish S.

1996-01-01

We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the 'Barut Girardello' coherent states to the Kronecker Product of two non-compact groups. The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of 'pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting 'bi-pair coherent states' in the context of four-mode interactions in quantum optics.
Galaxy collisions and shocks in compact groups

NASA Astrophysics Data System (ADS)

O'Sullivan, Ewan

2017-09-01

Evidence from IR, X-ray and HI studies suggests that low mass compact groups represent a key evolutionary stage in which shocks caused by galaxy interactions drive both the transformation of gas-rich spirals into early-type galaxies, and the build-up of the hot IGM. We have selected five groups where extensive multi-wavelength data shows violent ongoing galaxy interactions. We now propose to observe them with Chandra and XMM, searching for or confirming the presence of shocks in the X-ray IGM, measuring their strength and ability to heat cold gas, and examining the impact of galaxy/IGM interactions on galaxy transformation. Combined with our IR, CO, HI and optical IFU data, these observations will provide an exceptionally detailed view of this critical stage of galaxy and group evolution.
Advanced Accelerators for Medical Applications

NASA Astrophysics Data System (ADS)

Uesaka, Mitsuru; Koyama, Kazuyoshi

We review advanced accelerators for medical applications with respect to the following key technologies: (i) higher RF electron linear accelerator (hereafter “linac”); (ii) optimization of alignment for the proton linac, cyclotron and synchrotron; (iii) superconducting magnet; (iv) laser technology. Advanced accelerators for medical applications are categorized into two groups. The first group consists of compact medical linacs with high RF, cyclotrons and synchrotrons downsized by optimization of alignment and superconducting magnets. The second group comprises laser-based acceleration systems aimed of medical applications in the future. Laser plasma electron/ion accelerating systems for cancer therapy and laser dielectric accelerating systems for radiation biology are mentioned. Since the second group has important potential for a compact system, the current status of the established energy and intensity and of the required stability are given.
Advanced Accelerators for Medical Applications

NASA Astrophysics Data System (ADS)

Uesaka, Mitsuru; Koyama, Kazuyoshi

We review advanced accelerators for medical applications with respect to the following key technologies: (i) higher RF electron linear accelerator (hereafter "linac"); (ii) optimization of alignment for the proton linac, cyclotron and synchrotron; (iii) superconducting magnet; (iv) laser technology. Advanced accelerators for medical applications are categorized into two groups. The first group consists of compact medical linacs with high RF, cyclotrons and synchrotrons downsized by optimization of alignment and superconducting magnets. The second group comprises laserbased acceleration systems aimed of medical applications in the future. Laser plasma electron/ion accelerating systems for cancer therapy and laser dielectric accelerating systems for radiation biology are mentioned. Since the second group has important potential for a compact system, the current status of the established energy and intensity and of the required stability are given.
Generalized classical and quantum signal theories

NASA Astrophysics Data System (ADS)

Rundblad, E.; Labunets, V.; Novak, P.

2005-05-01

In this paper we develop two topics and show their inter- and cross-relation. The first centers on general notions of the generalized classical signal theory on finite Abelian hypergroups. The second concerns the generalized quantum hyperharmonic analysis of quantum signals (Hermitean operators associated with classical signals). We study classical and quantum generalized convolution hypergroup algebras of classical and quantum signals.
The Fock-Schwinger gauge in the BFV formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barcelos-Neto, J.; Galvao, C.A.P.; Gaete, P.

1991-06-07

The authors consider the implementation of a properly modified form of the Fock-Schwinger gauge condition in a general non-Abelian gauge theory in the context of the BFV formalism. In this paper arguments are presented to justify the necessity of modifying the original Fock-Schwinger condition. The free field propagator and the general Ward identity are also calculated.
Chern-Simons theory on a hypersphere

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.

1990-08-01

We demonstrate that a non-Abelian Chern-Simons field theory can be mapped from three-dimensional Euclidean space onto the surface of a sphere in four dimensions using a stereographic projection. The theory is manifestly invariant under a rotation on the four-dimensional hypersphere. An explicit one-loop calculation shows that the curvature of the hypersphere induces a conformal anomaly.
Duality, marginal perturbations, and gauging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henningson, M.; Nappi, C.R.

1993-07-15

We study duality transformations for two-dimensional [sigma] models with Abelian chiral isometries and prove that generic such transformations are equivalent to integrated marginal perturbations by bilinears in the chiral currents, thus confirming a recent conjecture by Hassan and Sen formulated in the context of Wess-Zumino-Witten models. Specific duality transformations instead give rise to coset models plus free bosons.

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