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

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.

Loop corrections in double field theory: non-trivial dilaton potentials

NASA Astrophysics Data System (ADS)

Lv, Songlin; Wu, Houwen; Yang, Haitang

2014-10-01

It is believed that the invariance of the generalised diffeomorphisms prevents any non-trivial dilaton potential from double field theory. It is therefore difficult to include loop corrections in the formalism. We show that by redefining a non-local dilaton field, under strong constraint which is necessary to preserve the gauge invariance of double field theory, the theory does permit non-constant dilaton potentials and loop corrections. If the fields have dependence on only one single coordinate, the non-local dilaton is identical to the ordinary one with an additive constant.

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.

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.

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

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.

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.

Non-Abelian supertubes

NASA Astrophysics Data System (ADS)

Fernández-Melgarejo, José J.; Park, Minkyu; Shigemori, Masaki

2017-12-01

A supertube is a supersymmetric configuration in string theory which occurs when a pair of branes spontaneously polarizes and generates a new dipole charge extended along a closed curve. The dipole charge of a codimension-2 supertube is characterized by the U-duality monodromy as one goes around the supertube. For multiple codimension-2 supertubes, their monodromies do not commute in general. In this paper, we construct a supersymmetric solution of five-dimensional supergravity that describes two supertubes with such non-Abelian monodromies, in a certain perturbative expansion. In supergravity, the monodromies are realized as the multi-valuedness of the scalar fields, while in higher dimensions they correspond to non-geometric duality twists of the internal space. The supertubes in our solution carry NS5 and 5 2 2 dipole charges and exhibit the same monodromy structure as the SU(2) Seiberg-Witten geometry. The perturbative solution has AdS2 × S 2 asymptotics and vanishing four-dimensional angular momentum. We argue that this solution represents a microstate of four-dimensional black holes with a finite horizon and that it provides a clue for the gravity realization of a pure-Higgs branch state in the dual quiver quantum mechanics.

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

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.

Late time acceleration of the 3-space in a higher dimensional steady state universe in dilaton gravity

NASA Astrophysics Data System (ADS)

Akarsu, Özgür; Dereli, Tekin

2013-02-01

We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = ½ that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.

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.

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.

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 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.

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

Hamiltonian thermodynamics of three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.

2008-08-15

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free {omega} parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcationmore » 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates (M,P{sub M}), M being the mass parameter and P{sub M} its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.« less

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

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.

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.

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 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

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

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 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

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.

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.

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.

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.

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.

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

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.

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.

Dilatonic parallelizable NS-NS backgrounds

NASA Astrophysics Data System (ADS)

Kawano, Teruhiko; Yamaguchi, Satoshi

2003-08-01

We complete the classification of parallelizable NS-NS backgrounds in type II supergravity by adding the dilatonic case to the result of Figueroa-O'Farrill on the non-dilatonic case. We also study the supersymmetry of these parallelizable backgrounds. It is shown that all the dilatonic parallelizable backgrounds have sixteen supersymmetries.

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.

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.

Symmetries, holography, and quantum phase transition in two-dimensional dilaton AdS gravity

NASA Astrophysics Data System (ADS)

Cadoni, Mariano; Ciulu, Matteo; Tuveri, Matteo

2018-05-01

We revisit the Almheiri-Polchinski dilaton gravity model from a two-dimensional (2D) bulk perspective. We describe a peculiar feature of the model, namely the pattern of conformal symmetry breaking using bulk Killing vectors, a covariant definition of mass and the flow between different vacua of the theory. We show that the effect of the symmetry breaking is both the generation of an infrared scale (a mass gap) and to make local the Goldstone modes associated with the asymptotic symmetries of the 2D spacetime. In this way a nonvanishing central charge is generated in the dual conformal theory, which accounts for the microscopic entropy of the 2D black hole. The use of covariant mass allows to compare energetically the two different vacua of the theory and to show that at zero temperature the vacuum with a constant dilaton is energetically preferred. We also translate in the bulk language several features of the dual CFT discussed by Maldacena et al. The uplifting of the 2D model to (d +2 )-dimensional theories exhibiting hyperscaling violation is briefly discussed.

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.

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.

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.

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.

A soft-wall dilaton

DOE PAGES

Cox, Peter; Gherghetta, Tony

2015-02-02

Here, we study the properties of the dilaton in a soft-wall background using two solutions of the Einstein equations. These solutions contain an asymptotically AdS metric with a nontrivial scalar profile that causes both the spontaneous breaking of conformal invariance and the generation of a mass gap in the particle spectrum. We first present an analytic solution, using the superpotential method, that describes a CFT spontaneously broken by a finite dimensional operator in which a light dilaton mode appears in the spectrum. This represents a tuning in the vanishing of the quartic coupling in the effective potential that could bemore » naturally realised from an underlying supersymmetry. Instead, by considering a generalised analytic scalar bulk potential that quickly transitions at the condensate scale from a walking coupling in the UV to an order-one β-function in the IR, we obtain a naturally light dilaton. This provides a simple example for obtaining a naturally light dilaton from nearly-marginal CFT deformations in the more realistic case of a soft-wall background.« less

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

Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes

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

Dias, Goncalo A. S.; Lemos, Jose P. S.; Centro Multidisciplinar de Astrofisica-CENTRA, Departamento de Fisica, Instituto Superior Tecnico-IST, Universidade Tecnica de Lisboa-UTL, Avenida Rovisco Pais 1, 1049-001 Lisboa

2008-10-15

The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free {omega} parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ({omega}{yields}{+-}{infinity}), a dimensionally reduced cylindrical four-dimensional general relativity theory ({omega}=0), and a theory representing a class of theories ({omega}=-3), all with a Maxwell term. The Hamiltonian formalismmore » is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P{sub M};Q,P{sub Q}), where M is the mass parameter, which for {omega}<-(3/2) and for {omega}={+-}{infinity} needs a careful renormalization, P{sub M} is the conjugate momenta of M, Q is the charge parameter, and P{sub Q} is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field {phi}. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of

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.

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

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.

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 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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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∘.

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.

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.

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.

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.

Z n clock models and chains of so(n)2 non-Abelian anyons: symmetries, integrable points and low energy properties

NASA Astrophysics Data System (ADS)

Finch, Peter E.; Flohr, Michael; Frahm, Holger

2018-02-01

We study two families of quantum models which have been used previously to investigate the effect of topological symmetries in one-dimensional correlated matter. Various striking similarities are observed between certain {Z}n quantum clock models, spin chains generalizing the Ising model, and chains of non-Abelian anyons constructed from the so(n)2 fusion category for odd n, both subject to periodic boundary conditions. In spite of the differences between these two types of quantum chains, e.g. their Hilbert spaces being spanned by tensor products of local spin states or fusion paths of anyons, the symmetries of the lattice models are shown to be closely related. Furthermore, under a suitable mapping between the parameters describing the interaction between spins and anyons the respective Hamiltonians share part of their energy spectrum (although their degeneracies may differ). This spin-anyon correspondence can be extended by fine-tuning of the coupling constants leading to exactly solvable models. We show that the algebraic structures underlying the integrability of the clock models and the anyon chain are the same. For n  =  3,5,7 we perform an extensive finite size study—both numerical and based on the exact solution—of these models to map out their ground state phase diagram and to identify the effective field theories describing their low energy behaviour. We observe that the continuum limit at the integrable points can be described by rational conformal field theories with extended symmetry algebras which can be related to the discrete ones of the lattice models.

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.

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.

Dilaton field released under collision of dilatonic black holes with Gauss-Bonnet term

NASA Astrophysics Data System (ADS)

Gwak, Bogeun; Ro, Daeho

2017-08-01

We investigate the upper limit of the gravitational radiation released upon the collision of two dilatonic black holes by analyzing the Gauss-Bonnet term. Dilatonic black holes have a dilaton hair coupled with this term. Using the laws of thermodynamics, the upper limit of the radiation is obtained, which reflected the effects of the dilaton hair. The amount of radiation released is greater than that emitted by a Schwarzschild black hole due to the contribution from the dilaton hair. In the collision, most of the dilaton hair can be released through radiation, where the energy radiated by the dilaton hair is maximized when the horizon of one black hole is minimized for a fixed second black hole.

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.

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.

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.

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.

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.

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.

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

Radiation and the classical double copy for color charges

NASA Astrophysics Data System (ADS)

Goldberger, Walter D.; Ridgway, Alexander K.

2017-06-01

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson, these are shown to generate solutions of d -dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

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.

Fermions tunnelling from the charged dilatonic black holes

NASA Astrophysics Data System (ADS)

Chen, De-You; Jiang, Qing-Quan; Zu, Xiao-Tao

2008-10-01

Kerner and Mann's recent work shows that for an uncharged and non-rotating black hole its Hawking temperature can be correctly derived by fermions tunnelling from its horizons. In this paper, our main work is to improve the analysis to deal with charged fermion tunnelling from the general dilatonic black holes, specifically including the charged, spherically symmetric dilatonic black hole, the rotating Einstein Maxwell dilaton axion (EMDA) black hole and the rotating Kaluza Klein (KK) black hole. As a result, the correct Hawking temperatures are well recovered by charged fermions tunnelling from these black holes.

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.

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.

Dilaton-assisted dark matter.

PubMed

Bai, Yang; Carena, Marcela; Lykken, Joseph

2009-12-31

A dilaton could be the dominant messenger between standard model fields and dark matter. The measured dark matter relic abundance relates the dark matter mass and spin to the conformal breaking scale. The dark matter-nucleon spin-independent cross section is predicted in terms of the dilaton mass. We compute the current constraints on the dilaton from LEP and Tevatron experiments, and the gamma-ray signal from dark matter annihilation to dilatons that could be observed by Fermi Large Area Telescope.

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.

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.

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.

Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.

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

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.

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.

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.

Cohomogeneity-one solutions in Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Lim, Yen-Kheng

2017-05-01

The field equations for Einstein-Maxwell-dilaton gravity in D dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With this procedure, we present interesting solutions such as a one-parameter generalization of the dilaton-Melvin spacetime and a three-parameter solution that interpolates between the Reissner-Nordström and Bertotti-Robinson solutions. This procedure also allows simple, alternative derivations of known solutions such as the Lifshitz spacetime and the planar anti-de Sitter naked singularity. In the latter case, the metric is cast in a simpler form which reveals the presence of an additional curvature singularity.

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.

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.

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

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.

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.

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.

Thermodynamics of new black hole solutions in the Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Dehghani, M.

In the present work, thermodynamics of the new black hole solutions to the four-dimensional Einstein-Maxwell-dilaton gravity theory have been studied. The dilaton potential, as the solution to the scalar field equations, has been constructed out by a linear combination of three Liouville-type potentials. Three new classes of charged dilatonic black hole solutions, as the exact solutions to the coupled equations of gravitational, electromagnetic and scalar fields, have been introduced. The conserved charge and mass of the new black holes have been calculated by utilizing Gauss's electric law and Abbott-Deser mass proposal, respectively. Also, the temperature, entropy and the electric potential of these new classes of charged dilatonic black holes have been calculated, making use of the geometrical approaches. Through a Smarr-type mass formula, the intensive parameters of the black holes have been calculated and validity of the first law of black hole thermodynamics has been confirmed. A thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. The heat capacity of the new black holes has been calculated and the points of type one- and type two-phase transitions as well as the ranges at which the new charged dilatonic black holes are locally stable have been determined, precisely.

Double-black-hole solutions of the Einstein-Maxwell-dilaton theory in five dimensions

NASA Astrophysics Data System (ADS)

Stelea, Cristian

2018-01-01

We describe a solution-generating technique that maps a static charged solution of the Einstein-Maxwell theory in four (or five) dimensions to a five-dimensional solution of the Einstein-Maxwell-Dilaton theory. As examples of this technique first we show how to construct the dilatonic version of the Reissner-Nordström solution in five dimensions and then we consider the more general case of the double black hole solutions and describe some of their properties. We found that in the general case the value of the conical singularities in between the black holes is affected by the dilaton's coupling constant to the gauge field and only in the particular case when all charges are proportional to the masses this dependence cancels out.

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.

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.

Three dimensional N=4 supersymmetric mechanics with Wu-Yang monopole

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

Bellucci, Stefano; Krivonos, Sergey; Sutulin, Anton

2010-05-15

We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential. This additional potential is completely fixed by N=4 supersymmetry, and in the simplest case of flat metrics it coincides with that which provides the existence of the Runge-Lenz vector for the bosonic subsector. The isospin degrees of freedom are described on the Lagrangian level by bosonic auxiliary variables forming N=4 supermultiplet with additional, also auxiliary, fermions. Being quite general, the constructed systems include such interesting cases as N=4 superconformally invariant systems withmore » Wu-Yang monopole, the particles living in the flat R{sup 3} and in the RxS{sup 2} spaces and interacting with the monopole, and also the particles moving on three-dimensional sphere and pseudosphere with the Wu-Yang monopole sitting in the center. The superfield Lagrangian description of these systems is so simple that one could wonder to see how all couplings and the proper coefficients arise while passing to the component action.« less

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…

Thermodynamics of charged dilatonic BTZ black holes in rainbow gravity

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-02-01

In this paper, the charged three-dimensional Einstein's theory coupled to a dilatonic field has been considered in the rainbow gravity. The dilatonic potential has been written as the linear combination of two Liouville-type potentials. Four new classes of charged dilatonic rainbow black hole solutions, as the exact solution to the coupled field equations of the energy dependent space time, have been obtained. Two of them are correspond to the Coulomb's electric field and the others are consequences of a modified Coulomb's law. Total charge and mass as well as the entropy, temperature and electric potential of the new charged black holes have been calculated in the presence of rainbow functions. Although the thermodynamic quantities are affected by the rainbow functions, it has been found that the first law of black hole thermodynamics is still valid for all of the new black hole solutions. At the final stage, making use of the canonical ensemble method and regarding the black hole heat capacity, the thermal stability or phase transition of the new rainbow black hole solutions have been analyzed.

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

Dilaton Cosmology and Phenomenology

NASA Astrophysics Data System (ADS)

Gasperini, M.

This paper is dedicated to Gabriele Veneziano on his 65th birthday. Most of the results reported here are known results, due to Gabriele, or obtained in collaboration with him, or inspired by our joint work on string cosmology. A few new results are also presented concerning the duality invariance of a non-local dilaton coupling to the matter sources, and its possible cosmological applications in the context of the dark energy scenario.

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.

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.

On the Liouville 2D dilaton gravity models with sinh-Gordon matter

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Zelnikov, Andrei

2018-02-01

We study 1 + 1 dimensional dilaton gravity models which take into account backreaction of the sinh-Gordon matter field. We found a wide class of exact solutions which generalizes black hole solutions of the Jackiw-Teitelboim gravity model and its hyperbolic deformation.

From N=4 Galilean superparticle to three-dimensional non-relativistic N=4 superfields

NASA Astrophysics Data System (ADS)

Fedoruk, Sergey; Ivanov, Evgeny; Lukierski, Jerzy

2018-05-01

We consider the general N=4 , d = 3 Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for N=4 three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic κ-gauge transformations. The quantization of the model gives rise to the collection of free N=4 , d = 3 Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic N=4 supersymmetric theories.

Analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

We construct an analytical approximation for the numerical black hole metric of P. Kanti et al. [Phys. Rev. D 54, 5049 (1996), 10.1103/PhysRevD.54.5049] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and a good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks, and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

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…

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.

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

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.

Confinement Driven by Scalar Field in 4d Non Abelian Gauge Theories

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

Chabab, Mohamed

2007-01-12

We review some of the most recent work on confinement in 4d gauge theories with a massive scalar field (dilaton). Emphasis is put on the derivation of confining analytical solutions to the Coulomb problem versus dilaton effective couplings to gauge terms. It is shown that these effective theories can be relevant to model quark confinement and may shed some light on confinement mechanism. Moreover, the study of interquark potential, derived from Dick Model, in the heavy meson sector proves that phenomenological investigation of tmechanism is more than justified and deserves more efforts.

Dilaton vs Higgs: Nearly Conformal Physics

NASA Astrophysics Data System (ADS)

Kozlov, G. A.

2016-04-01

We consider the model in which the conformal symmetry can be broken spontaneously, and a light scalar dilaton could emerge in the low-energy spectrum. The contribution of the dark photon production relevant to two photons decays of a Higgs boson/dilaton is discussed.

Thermodynamics of novel charged dilatonic BTZ black holes

NASA Astrophysics Data System (ADS)

Dehghani, M.

2017-10-01

In this paper, the three-dimensional Einstein-Maxwell theory in the presence of a dilatonic scalar field has been studied. It has been shown that the dilatonic potential must be considered as the linear combination of two Liouville-type potentials. Two new classes of charged dilatonic BTZ black holes, as the exact solutions to the coupled scalar, vector and tensor field equations, have been obtained and their properties have been studied. The conserved charge and mass of the new black holes have been calculated, making use of the Gauss's law and Abbott-Deser proposal, respectively. Through comparison of the thermodynamical extensive quantities (i.e. temperature and entropy) obtained from both, the geometrical and the thermodynamical methods, the validity of the first law of black hole thermodynamics has been confirmed for both of the new black holes we just obtained. A black hole thermal stability or phase transition analysis has been performed, making use of the canonical ensemble method. Regarding the black hole heat capacity, it has been found that for either of the new black hole solutions there are some specific ranges in such a way that the black holes with the horizon radius in these ranges are locally stable. The points of type one and type two phase transitions have been determined. The black holes, with the horizon radius equal to the transition points are unstable. They undergo type one or type two phase transitions to be stabilized.

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

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.

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.

The twelve-flavor β-function and dilaton tests of the sextet scalar

NASA Astrophysics Data System (ADS)

Fodor, Zoltan; Holland, Kieran; Kuti, Julius; Nogradi, Daniel; Him Wong, Chik

2018-03-01

We discuss near-conformal gauge theories beyond the standard model (BSM) where interesting results on the twelve-flavor β-function of massless fermions in the fundamental representation of the SU(3) color gauge group and dilaton tests of the light scalar with two massless fermions in the two-index symmetric tensor (sextet) representation can be viewed as parts of the same BSM paradigm under investigation. The clear trend in the decreasing size of β-functions at fixed renormalized gauge coupling is interpreted as a first indicator how the conformal window (CW) is approached in correlation with emergent near-conformal light scalars. BSM model building close to the CW will be influenced by differing expectations on the properties of the emergent light 0++ scalar either as a σ-particle of chiral symmetry breaking (ΧS B), or as a dilaton of scale symmetry breaking. The twelve-flavor β-function emerges as closest to the CW, perhaps near-conformal, or perhaps with an infrared fixed point (IRFP) at some unexplored strong coupling inside the CW. It is premature to speculate on dilaton properties of the twelveflavor model since the near-conformal realization remains an open question. However, it is interesting and important to investigate dilaton tests of the light sextet scalar whose β-function is closest to the CW in the symmetry breaking phase and emerges as the leading candidate for dilaton tests of the light scalar. We report results from high precision analysis of the twelve-flavor β-function [1] refuting its published IRFP [2, 3]. We present our objections to recent claims [4, 5] for non-universal behavior of staggered fermions used in our analysis. We also report our first analysis of dilaton tests of the light 0++ scalar in the sextet model and comment on related post-conference developments. The dilaton test is the main thrust of this conference contribution including presentation #405 on the nf = 12 β-function and presentation #260 on dilaton tests of the

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.

Very light dilaton and naturally light Higgs boson

NASA Astrophysics Data System (ADS)

Hong, Deog Ki

2018-02-01

We study very light dilaton, arising from a scale-invariant ultraviolet theory of the Higgs sector in the standard model of particle physics. Imposing the scale symmetry below the ultraviolet scale of the Higgs sector, we alleviate the fine-tuning problem associated with the Higgs mass. When the electroweak symmetry is spontaneously broken radiatively à la Coleman-Weinberg, the dilaton develops a vacuum expectation value away from the origin to give an extra contribution to the Higgs potential so that the Higgs mass becomes naturally around the electroweak scale. The ultraviolet scale of the Higgs sector can be therefore much higher than the electroweak scale, as the dilaton drives the Higgs mass to the electroweak scale. We also show that the light dilaton in this scenario is a good candidate for dark matter of mass m D ˜ 1 eV - 10 keV, if the ultraviolet scale is about 10-100 TeV. Finally we propose a dilaton-assisted composite Higgs model to realize our scenario. In addition to the light dilaton the model predicts a heavy U(1) axial vector boson and two massive, oppositely charged, pseudo Nambu-Goldstone bosons, which might be accessible at LHC.

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

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

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

Motion and collision of particles in a rotating linear dilaton black hole

NASA Astrophysics Data System (ADS)

González, P. A.; Olivares, Marco; Papantonopoulos, Eleftherios; Vásquez, Yerko

2018-03-01

We study the motion of particles in the background of a four-dimensional linear dilaton black hole. We solve analytically the equations of motion of the test particles, and we describe their motion. We show that the dilaton black hole acts as a particle accelerator by analyzing the energy in the center of mass frame of two colliding particles in the vicinity of its horizon. In particular, we find that there is a critical value of the angular momentum, which depends on the string coupling, and a particle with this critical angular momentum can reach the inner horizon with an arbitrarily high c.m. energy. This is known as the Bañados, Silk, and West process. We also show that the motion and collisions of particles have behavior similar to the three-dimensional Bañados-Teitelboim-Zanelli black hole. In fact, the photons can plunge into the horizon or escape to infinity, and they cannot be deflected, while for massive particles there are no confined orbits of the first kind, like planetary or circular orbits.

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.

Quasinormal Modes of Charged Dilaton Black Holes and Their Entropy Spectra

NASA Astrophysics Data System (ADS)

Sakalli, I.

2013-08-01

In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter a, it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNM in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these black holes (BHs). Although the QNM frequencies are tuned by a, we show that the quantum spectra do not depend on a, and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant ɛ is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.

Type IIB supergravity solution for the T-dual of the η-deformed AdS 5 × S 5 superstring

NASA Astrophysics Data System (ADS)

Hoare, B.; Tseytlin, A. A.

2015-10-01

We find an exact type IIB supergravity solution that represents a one-parameter deformation of the T-dual of the AdS 5 × S 5 background (with T-duality applied in all 6 abelian bosonic isometric directions). The non-trivial fields are the metric, dilaton and RR 5-form only. The latter has remarkably simple "undeformed" form when written in terms of a "deformation-rotated" vielbein basis. An unusual feature of this solution is that the dilaton contains a linear dependence on the isometric coordinates of the metric precluding a straightforward reversal of T-duality. If we still formally dualize back, we find exactly the metric, B-field and product of dilaton with RR field strengths as recently extracted from the η-deformed AdS 5 × S 5 superstring action in arXiv:1507.04239. We also discuss similar solutions for deformed AdS n × S n backgrounds with n = 2 , 3. In the η → i limit we demonstrate that all these backgrounds can be interpreted as special limits of gauged WZW models and are also related to (a limit of) the Pohlmeyer-reduced models of the AdS n × S n superstrings.

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.

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

Exact Solutions in Three-Dimensional Gravity

NASA Astrophysics Data System (ADS)

García-Díaz, Alberto A.

2017-09-01

Preface; 1. Introduction; 2. Point particles; 3. Dust solutions; 4. AdS cyclic symmetric stationary solutions; 5. Perfect fluid static stars; 6. Static perfect fluid stars with Λ; 7. Hydrodynamic equilibrium; 8. Stationary perfect fluid with Λ; 9. Friedmann–Robertson–Walker cosmologies; 10. Dilaton-inflaton FRW cosmologies; 11. Einstein–Maxwell solutions; 12. Nonlinear electrodynamics black hole; 13. Dilaton minimally coupled to gravity; 14. Dilaton non-minimally coupled to gravity; 15. Low energy 2+1 string gravity; 16. Topologically massive gravity; 17. Bianchi type spacetimes in TMG; 18. Petrov type N wave metrics; 19. Kundt spacetimes in TMG; 20. Cotton tensor in Riemannian spacetimes; References; Index.

Two-dimensional non-volatile programmable p-n junctions

NASA Astrophysics Data System (ADS)

Li, Dong; Chen, Mingyuan; Sun, Zhengzong; Yu, Peng; Liu, Zheng; Ajayan, Pulickel M.; Zhang, Zengxing

2017-09-01

Semiconductor p-n junctions are the elementary building blocks of most electronic and optoelectronic devices. The need for their miniaturization has fuelled the rapid growth of interest in two-dimensional (2D) materials. However, the performance of a p-n junction considerably degrades as its thickness approaches a few nanometres and traditional technologies, such as doping and implantation, become invalid at the nanoscale. Here we report stable non-volatile programmable p-n junctions fabricated from the vertically stacked all-2D semiconductor/insulator/metal layers (WSe2/hexagonal boron nitride/graphene) in a semifloating gate field-effect transistor configuration. The junction exhibits a good rectifying behaviour with a rectification ratio of 104 and photovoltaic properties with a power conversion efficiency up to 4.1% under a 6.8 nW light. Based on the non-volatile programmable properties controlled by gate voltages, the 2D p-n junctions have been exploited for various electronic and optoelectronic applications, such as memories, photovoltaics, logic rectifiers and logic optoelectronic circuits.

Two-dimensional non-volatile programmable p-n junctions.

PubMed

Li, Dong; Chen, Mingyuan; Sun, Zhengzong; Yu, Peng; Liu, Zheng; Ajayan, Pulickel M; Zhang, Zengxing

2017-09-01

Semiconductor p-n junctions are the elementary building blocks of most electronic and optoelectronic devices. The need for their miniaturization has fuelled the rapid growth of interest in two-dimensional (2D) materials. However, the performance of a p-n junction considerably degrades as its thickness approaches a few nanometres and traditional technologies, such as doping and implantation, become invalid at the nanoscale. Here we report stable non-volatile programmable p-n junctions fabricated from the vertically stacked all-2D semiconductor/insulator/metal layers (WSe 2 /hexagonal boron nitride/graphene) in a semifloating gate field-effect transistor configuration. The junction exhibits a good rectifying behaviour with a rectification ratio of 10 4 and photovoltaic properties with a power conversion efficiency up to 4.1% under a 6.8 nW light. Based on the non-volatile programmable properties controlled by gate voltages, the 2D p-n junctions have been exploited for various electronic and optoelectronic applications, such as memories, photovoltaics, logic rectifiers and logic optoelectronic circuits.

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.

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.

A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure

NASA Astrophysics Data System (ADS)

Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.

2016-08-01

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Asymptotically (A)dS dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Hajkhalili, S.; Sheykhi, A.

It is well known that with an appropriate combination of three Liouville-type dilaton potentials, one can construct charged dilaton black holes in an (anti)-de Sitter [(A)dS] spaces in the presence of linear Maxwell field. However, asymptotically (A)dS dilaton black holes coupled to nonlinear gauge field have not been found. In this paper, we construct, for the first time, three new classes of dilaton black hole solutions in the presence of three types of nonlinear electrodynamics, namely Born-Infeld (BI), Logarithmic (LN) and Exponential nonlinear (EN) electrodynamics. All these solutions are asymptotically (A)dS and in the linear regime reduce to the Einstein-Maxwell-dilaton (EMd) black holes in (A)dS spaces. We investigate physical properties and the causal structure, as well as asymptotic behavior of the obtained solutions, and show that depending on the values of the metric parameters, the singularity can be covered by various horizons. We also calculate conserved and thermodynamic quantities of the obtained solutions. Interestingly enough, we find that the coupling of dilaton field and nonlinear gauge field in the background of (A)dS spaces leads to a strange behavior for the electric field. We observe that the electric field is zero at singularity and increases smoothly until reaches a maximum value, then it decreases smoothly until goes to zero as r →∞. The maximum value of the electric field increases with increasing the nonlinear parameter β or decreasing the dilaton coupling α and is shifted to the singularity in the absence of either dilaton field (α = 0) or nonlinear gauge field (β →∞).

$$ \\mathcal{N}=1 $$ 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

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

Dilaton black holes in the de Sitter or anti-de Sitter universe

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

Gao Changjun; Zhang Shuangnan; Physics Department, University of Alabama, Huntsville, Alabama 35899

2004-12-15

Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti-de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. In this work we obtain the dilaton black-hole solutions in the background of the de Sitter or anti-de Sitter universe, with the combination of three Liouville-type dilaton potentials.

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, 2

Small dark energy and stable vacuum from Dilaton-Gauss-Bonnet coupling in TMT

NASA Astrophysics Data System (ADS)

Guendelman, Eduardo I.; Nishino, Hitoshi; Rajpoot, Subhash

2017-04-01

In two measures theories (TMT), in addition to the Riemannian measure of integration, being the square root of the determinant of the metric, we introduce a metric-independent density Φ in four dimensions defined in terms of scalars \\varphi _a by Φ =\\varepsilon ^{μ ν ρ σ } \\varepsilon _{abcd} (partial _{μ }\\varphi _a)(partial _{ν }\\varphi _b) (partial _{ρ }\\varphi _c) (partial _{σ }\\varphi _d). With the help of a dilaton field φ we construct theories that are globally scale invariant. In particular, by introducing couplings of the dilaton φ to the Gauss-Bonnet (GB) topological density {√{-g}} φ ( R_{μ ν ρ σ }^2 - 4 R_{μ ν }^2 + R^2 ) we obtain a theory that is scale invariant up to a total divergence. Integration of the \\varphi _a field equation leads to an integration constant that breaks the global scale symmetry. We discuss the stabilizing effects of the coupling of the dilaton to the GB-topological density on the vacua with a very small cosmological constant and the resolution of the `TMT Vacuum-Manifold Problem' which exists in the zero cosmological-constant vacuum limit. This problem generically arises from an effective potential that is a perfect square, and it gives rise to a vacuum manifold instead of a unique vacuum solution in the presence of many different scalars, like the dilaton, the Higgs, etc. In the non-zero cosmological-constant case this problem disappears. Furthermore, the GB coupling to the dilaton eliminates flat directions in the effective potential, and it totally lifts the vacuum-manifold degeneracy.

Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea

NASA Astrophysics Data System (ADS)

Dahan, Daniel; Tanhayi Ahari, Mostafa; Ortiz, Gerardo; Seradjeh, Babak; Grosfeld, Eytan

We study the quantum dynamics of Majorana and regular fermion bound states coupled to a one-dimensional lead. The dynamics following the quench in the coupling to the lead exhibits a series of dynamical revivals as the bound state propagates in the lead and reflects from the boundaries. We show that the nature of revivals for a single Majorana bound state depends uniquely on the presence of a resonant level in the lead. When two spatially separated Majorana modes are coupled to the lead, the revivals depend only on the phase difference between their host superconductors. Remarkably, the quench in this case effectively performs a fermion-parity interferometry between Majorana bound states, revealing their unique non-Abelian braiding. Using both analytical and numerical techniques, we find the pattern of fermion parity transfers following the quench, study its evolution in the presence of disorder and interactions, and thus, ascertain the fate of Majorana in a rough Fermi sea. Work supported in part by BSF Grant No. 2014345, ISF Grant Nos. 401/12 and 1626/16, EU Seventh Framework Programme (FP7/2007-2013) Grant No. 303742, NSF CAREER Grant DMR-1350663 and the College of Arts and Sciences at Indiana University.

Compact static stars in minimal dilatonic gravity

NASA Astrophysics Data System (ADS)

Fiziev, Plamen P.

2017-09-01

In the version1 of this paper we presented for the first time the basic equations and relations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG). This model is locally equivalent to the f(R) theory of gravity and gives an alternative description of the effects of dark matter and dark energy using the Brans-Dicke dilaton Φ. To outline the basic properties of the MDG model of SSSS and to compare them with general relativistic results, in this paper we use the relativistic equation of state (EOS) of neutron matter as an ideal Fermi neutron gas at zero temperature. We overcome the well-known difficulties of the physics of SSSS in the f(R) theories of gravity2,3 applying novel highly nontrivial nonlinear boundary conditions, which depend on the global properties of the solution and on the EOS. We also introduce two pairs of new notions: cosmological-energy-pressure densities and dilaton-energy-pressure densities, as well as two new EOSs for them: cosmological EOS (CEOS) and dilaton EOS (DEOS). Special attention is paid to the dilatonic sphere (in brief — disphere) of SSSS, introduced in this paper for the first time. Using several realistic EOS for neutron star (NS): SLy, BSk19, BSk20 and BSk21, and current observational two-solar-masses-limit, we derive an estimate for scalar-field-mass mΦ ˜ 10-13eV/c2 ÷ 4 × 10-11eV/c2. Thus, the present version of the paper reflects some of the recent developments of the topic.

Dilatonic imprints on exact gravitational wave signatures

NASA Astrophysics Data System (ADS)

McCarthy, Fiona; KubizÅák, David; Mann, Robert B.

2018-05-01

By employing the moduli space approximation, we analytically calculate the gravitational wave signatures emitted upon the merger of two extremally charged dilatonic black holes. We probe several values of the dilatonic coupling constant a , and find significant departures from the Einstein-Maxwell (a =0 ) counterpart studied in [Phys. Rev. D 96, 061501 (2017), 10.1103/PhysRevD.96.061501]. For (low-energy) string theory black holes (a =1 ) there are no coalescence orbits and only a memory effect is observed, whereas for an intermediate value of the coupling (a =1 /√{3 } ) the late-time merger signature becomes exponentially suppressed, compared to the polynomial decay in the a =0 case without a dilaton. Such an imprint shows a clear difference between the case with and without a scalar field (as, for example, predicted by string theory) in black hole mergers.

Numerical calculation of the entanglement entropy for scalar field in dilaton spacetimes

NASA Astrophysics Data System (ADS)

Huang, Shifeng; Fang, Xiongjun; Jing, Jiliang

2018-06-01

Using coupled harmonic oscillators model, we numerical analyze the entanglement entropy of massless scalar field in Gafinkle-Horowitz-Strominger (GHS) dilaton spacetime and Gibbons-Maeda (GM) dilaton spacetime. By numerical fitting, we find that the entanglement entropy of the dilaton black holes receive contribution from dilaton charge and is proportional to the area of the event horizon. It is interesting to note that the results of numerical fitting are coincide with ones obtained by using brick wall method and Euclidean path integral approach.

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 .

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

Searching for dilaton dark matter with atomic clocks

NASA Astrophysics Data System (ADS)

Arvanitaki, Asimina; Huang, Junwu; Van Tilburg, Ken

2015-01-01

We propose an experiment to search for ultralight scalar dark matter (DM) with dilatonic interactions. Such couplings can arise for the dilaton as well as for moduli and axion-like particles in the presence of C P violation. Ultralight dilaton DM acts as a background field that can cause tiny but coherent oscillations in Standard Model parameters such as the fine-structure constant and the proton-electron mass ratio. These minute variations can be detected through precise frequency comparisons of atomic clocks. Our experiment extends current searches for drifts in fundamental constants to the well-motivated high-frequency regime. Our proposed setups can probe scalars lighter than 1 0-15 eV with a discovery potential of dilatonic couplings as weak as 1 0-11 times the strength of gravity, improving current equivalence principle bounds by up to 8 orders of magnitude. We point out potential 1 04 sensitivity enhancements with future optical and nuclear clocks, as well as possible signatures in gravitational-wave detectors. Finally, we discuss cosmological constraints and astrophysical hints of ultralight scalar DM, and show they are complimentary to and compatible with the parameter range accessible to our proposed laboratory experiments.

N = 1 supersymmetric indices and the four-dimensional A-model

NASA Astrophysics Data System (ADS)

Closset, Cyril; Kim, Heeyeon; Willett, Brian

2017-08-01

We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on M_4\\cong M_{g,p}× {S}^1 , a principal elliptic fiber bundle of degree p over a genus- g Riemann surface, Σ g . Equivalently, we compute the generalized supersymmetric index I_{M}{_{g,p}, with the supersymmetric three-manifold M_{g,p} as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Σ g . This A-model — or A-twisted two-dimensional N = (2 , 2) gauge theory — encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T 2 inside Σ g × T 2. Being defined by compactification on the torus, the A-model also enjoys natural modular properties, governed by the four-dimensional 't Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.

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.

Primordial perturbations from dilaton-induced gauge fields

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

Choi, Kiwoon; Choi, Ki-Young; Kim, Hyungjin

2015-10-01

We study the primordial scalar and tensor perturbations in inflation scenario involving a spectator dilaton field. In our setup, the rolling spectator dilaton causes a tachyonic instability of gauge fields, leading to a copious production of gauge fields in the superhorizon regime, which generates additional scalar and tensor perturbations through gravitational interactions. Our prime concern is the possibility to enhance the tensor-to-scalar ratio r relative to the standard result, while satisfying the observational constraints. To this end, we allow the dilaton field to be stabilized before the end of inflation, but after the CMB scales exit the horizon. We showmore » that for the inflaton slow roll parameter ε ∼> 10{sup −3}, the tensor-to-scalar ratio in our setup can be enhanced only by a factor of O(1) compared to the standard result. On the other hand, for smaller ε corresponding to a lower inflation energy scale, a much bigger enhancement can be achieved, so that our setup can give rise to an observably large r∼> 10{sup −2} even when ε|| 10{sup −3}. The tensor perturbation sourced by the spectator dilaton can have a strong scale dependence, and is generically red-tilted. We also discuss a specific model to realize our scenario, and identify the parameter region giving an observably large r for relatively low inflation energy scales.« less

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.

Black hole dynamics in Einstein-Maxwell-dilaton theory

NASA Astrophysics Data System (ADS)

Hirschmann, Eric W.; Lehner, Luis; Liebling, Steven L.; Palenzuela, Carlos

2018-03-01

We consider the properties and dynamics of black holes within a family of alternative theories of gravity, namely Einstein-Maxwell-dilaton theory. We analyze the dynamical evolution of individual black holes as well as the merger of binary black hole systems. We do this for a wide range of parameter values for the family of Einstein-Maxwell-dilaton theories, investigating, in the process, the stability of these black holes. We examine radiative degrees of freedom, explore the impact of the scalar field on the dynamics of merger, and compare with other scalar-tensor theories. We argue that the dilaton can largely be discounted in understanding merging binary systems and that the end states essentially interpolate between charged and uncharged, rotating black holes. For the relatively small charge values considered here, we conclude that these black hole systems will be difficult to distinguish from their analogs within General Relativity.

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.

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

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.

Moduli stabilising in heterotic nearly Kähler compactifications

NASA Astrophysics Data System (ADS)

Klaput, Michael; Lukas, Andre; Matti, Cyril; Svanes, Eirik E.

2013-01-01

We study heterotic string compactifications on nearly Kähler homogeneous spaces, including the gauge field effects which arise at order α'. Using Abelian gauge fields, we are able to solve the Bianchi identity and supersymmetry conditions to this order. The four-dimensional external space-time consists of a domain wall solution with moduli fields varying along the transverse direction. We find that the inclusion of α' corrections improves the moduli stabilization features of this solution. In this case, one of the dilaton and the volume modulus asymptotes to a constant value away from the domain wall. It is further shown that the inclusion of non-perturbative effects can stabilize the remaining modulus and "lift" the domain wall to an AdS vacuum. The coset SU(3)/U(1)2 is used as an explicit example to demonstrate the validity of this AdS vacuum. Our results show that heterotic nearly Kähler compactifications can lead to maximally symmetric four-dimensional space-times at the non-perturbative level.

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Dayyani, Z.; Sheykhi, A.; Dehghani, M. H.; Hajkhalili, S.

2018-02-01

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of T>T_c, we have no phase transition. When T=T_c, the system admits a second-order phase transition, while for T=T_fdilaton field. This novel zeroth-order phase transition occurs due to a finite jump in the Gibbs free energy which is generated by the dilaton-electromagnetic coupling constant, α , for a certain range of pressure.

Effect of the dilaton on holographic complexity growth

NASA Astrophysics Data System (ADS)

An, Yu-Sen; Peng, Rong-Hui

2018-03-01

In this paper, we investigate the action growth in various backgrounds in Einstein-Maxwell-dilaton theory. We calculate the full time evolution of action growth in the anti-de Sitter dilaton black hole and find it approaches the late time bound from above. We investigate the black hole which is asymptotically Lifshitz and obtain its late time and full time behavior. We find the violation of Lloyd bound in the late time limit and show the full time behavior approaching the late time bound from above and exhibiting some new features for z sufficiently large.

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

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.

AdS 2 holographic dictionary

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

Cvetic, Mirjam; Papadimitriou, Ioannis

Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetriesmore » and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, the four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries�

AdS 2 holographic dictionary

DOE PAGES

Cvetic, Mirjam; Papadimitriou, Ioannis

2016-12-02

Here, we construct the holographic dictionary for both running and constant dilaton solutions of the two dimensional Einstein-Maxwell-Dilaton theory that is obtained by a circle reduction from Einstein-Hilbert gravity with negative cosmological constant in three dimensions. This specific model ensures that the dual theory has a well defined ultraviolet completion in terms of a two dimensional conformal field theory, but our results apply qualitatively to a wider class of two dimensional dilaton gravity theories. For each type of solutions we perform holographic renormalization, compute the exact renormalized one-point functions in the presence of arbitrary sources, and derive the asymptotic symmetriesmore » and the corresponding conserved charges. In both cases we find that the scalar operator dual to the dilaton plays a crucial role in the description of the dynamics. Its source gives rise to a matter conformal anomaly for the running dilaton solutions, while its expectation value is the only non trivial observable for constant dilaton solutions. The role of this operator has been largely overlooked in the literature. We further show that the only non trivial conserved charges for running dilaton solutions are the mass and the electric charge, while for constant dilaton solutions only the electric charge is non zero. However, by uplifting the solutions to three dimensions we show that constant dilaton solutions can support non trivial extended symmetry algebras, including the one found by Compère, Song and Strominger, in agreement with the results of Castro and Song. Finally, we demonstrate that any solution of this specific dilaton gravity model can be uplifted to a family of asymptotically AdS 2 × S 2 or conformally AdS 2 × S 2 solutions of the STU model in four dimensions, including non extremal black holes. As a result, the four dimensional solutions obtained by uplifting the running dilaton solutions coincide with the so called ‘subtracted geometries�

EFT for vortices with dilaton-dependent localized flux

NASA Astrophysics Data System (ADS)

Burgess, C. P.; Diener, Ross; Williams, M.

2015-11-01

We study how codimension-two objects like vortices back-react gravitationally with their environment in theories (such as 4D or higher-dimensional supergravity) where the bulk is described by a dilaton-Maxwell-Einstein system. We do so both in the full theory, for which the vortex is an explicit classical `fat brane' solution, and in the effective theory of `point branes' appropriate when the vortices are much smaller than the scales of interest for their back-reaction (such as the transverse Kaluza-Klein scale). We extend the standard Nambu-Goto description to include the physics of flux-localization wherein the ambient flux of the external Maxwell field becomes partially localized to the vortex, generalizing the results of a companion paper [4] from N=2 supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of "superspace non-locality" which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic N=2 model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

Thermal fluctuations of dilaton black holes in gravity's rainbow

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-06-01

In this work, thermodynamics and phase transition of some new dilaton black hole solutions have been explored in the presence of the rainbow functions. By introducing an energy dependent space time, the dilaton potential has been obtained as the linear combination of two Liouville-type potentials and three new classes of black hole solutions have been constructed. The conserved and thermodynamic quantities of the new dilaton black holes have been calculated in the energy dependent space times. It has been shown that, even if some of the thermodynamic quantities are affected by the rainbow functions, the thermodynamical first law still remains valid. Also, the impacts of rainbow functions on the stability or phase transition of the new black hole solutions have been investigated. Finally, the quantum gravitational effects on the thermodynamics and phase transition of the solutions have been studied through consideration of the thermal fluctuations.

Entropy Conservation of Linear Dilaton Black Holes in Quantum Corrected Hawking Radiation

NASA Astrophysics Data System (ADS)

Sakalli, I.; Halilsoy, M.; Pasaoglu, H.

2011-10-01

It has been shown recently that information is lost in the Hawking radiation of the linear dilaton black holes in various theories when applying the tunneling formalism of Parikh and Wilczek without considering quantum gravity effects. In this paper, we recalculate the emission probability by taking into account the log-area correction to the Bekenstein-Hawking entropy and the statistical correlation between quanta emitted. The crucial role of the quantum gravity effects on the information leakage and black hole remnant is highlighted. The entropy conservation of the linear dilaton black holes is discussed in detail. We also model the remnant as an extreme linear dilaton black hole with a pointlike horizon in order to show that such a remnant cannot radiate and its temperature becomes zero. In summary, we show that the information can also leak out of the linear dilaton black holes together with preserving unitarity in quantum mechanics.

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.

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.

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

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

Iron line spectroscopy with Einstein-dilaton-Gauss-Bonnet black holes

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh; Bambi, Cosimo; Kokkotas, Kostas D.; Konoplya, Roman A.

2018-06-01

Einstein-dilaton-Gauss-Bonnet gravity is a well-motivated alternative theory of gravity that emerges naturally from string theory. While black hole solutions have been known in this theory in numerical form for a while, an approximate analytical metric was obtained recently by some of us, which allows for faster and more detailed analysis. Here we test the accuracy of the analytical metric in the context of X-ray reflection spectroscopy. We analyze innermost stable circular orbits (ISCO) and relativistically broadened iron lines and find that both the ISCO and iron lines are determined sufficiently accurately up to the limit of the approximation. We also find that, though the ISCO increases by about 7% as dilaton coupling increases from zero to extremal values, the redshift at ISCO changes by less than 1%. Consequently, the shape of the iron line is much less sensitive to the dilaton charge than expected.

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.

Mass, angular momentum, and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

2014-02-01

Mass, angular momentum, and charge inequalities for axisymmetric maximal time-symmetric initial data invariant under an action of U(1) group, in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory, is established. We assume that a data set with two asymptotically flat regions is given on a smooth simply connected manifold. We also pay attention to the area momentum charge inequalities for a closed orientable two-dimensional spacelike surface embedded in the spacetime of the considered theory.

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

Rotating black holes in dilatonic Einstein-Gauss-Bonnet theory.

PubMed

Kleihaus, Burkhard; Kunz, Jutta; Radu, Eugen

2011-04-15

We construct generalizations of the Kerr black holes by including higher-curvature corrections in the form of the Gauss-Bonnet density coupled to the dilaton. We show that the domain of existence of these Einstein-Gauss-Bonnet-dilaton (EGBD) black holes is bounded by the Kerr black holes, the critical EGBD black holes, and the singular extremal EGBD solutions. The angular momentum of the EGBD black holes can exceed the Kerr bound. The EGBD black holes satisfy a generalized Smarr relation. We also compare their innermost stable circular orbits with those of the Kerr black holes and show the existence of differences which might be observable in astrophysical systems.

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.

Hawking radiation from dilatonic black holes via anomalies

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

Jiang Qingquan; Cai Xu; Wu Shuangqing

2007-03-15

Recently, Hawking radiation from a Schwarzschild-type black hole via a gravitational anomaly at the horizon has been derived by Robinson and Wilczek. Their result shows that, in order to demand general coordinate covariance at the quantum level to hold in the effective theory, the flux of the energy-momentum tensor required to cancel the gravitational anomaly at the horizon of the black hole is exactly equal to that of (1+1)-dimensional blackbody radiation at the Hawking temperature. In this paper, we attempt to apply the analysis to derive Hawking radiation from the event horizons of static, spherically symmetric dilatonic black holes withmore » arbitrary coupling constant {alpha}, and that from the rotating Kaluza-Klein ({alpha}={radical}(3)) as well as the Kerr-Sen ({alpha}=1) black holes via an anomalous point of view. Our results support Robinson and Wilczek's opinion. In addition, the properties of the obtained physical quantities near the extreme limit are qualitatively discussed.« less

Supergravity backgrounds for deformations of AdS n × S n supercoset string models

DOE PAGES

Lunin, O.; Roiban, R.; Tseytlin, A. A.

2014-12-11

We considermore » type IIB supergravity backgrounds corresponding to the deformed AdS n × S n × T 10 - 2 n supercoset string models of the type constructed in arXiv:1309.5850[2] which depend on one deformation parameter κ. In AdS 2 × S 2 case we find that the deformed metric can be extended to a full supergravity solution with non-trivial dilaton, RR scalar and RR 5-form strength. The solution depends on a free parameter a that should be chosen as a particular function of κ to correspond to the deformed supercoset model. In AdS 3 × S 3 case the full solution supported by the dilaton, RR scalar and RR 3-form strength exists only in the two special cases, a = 0 and a = 1 . We conjecture that there may be a more general one-parameter solution supported by several RR fields that for particular a = a ( κ ) corresponds to the supercoset model. In the most complicated deformed AdS 5 × S 5 case we were able to find only the expressions for the dilaton and the RR scalar. The full solution is likely to be supported by a combination of the 5-form and 3-form field strengths. We comment on the singularity structure of the resulting metric and exact dilaton field.« less

Supergravity backgrounds for deformations of AdS n × S n supercoset string models

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

Lunin, O.; Roiban, R.; Tseytlin, A. A.

We considermore » type IIB supergravity backgrounds corresponding to the deformed AdS n × S n × T 10 - 2 n supercoset string models of the type constructed in arXiv:1309.5850[2] which depend on one deformation parameter κ. In AdS 2 × S 2 case we find that the deformed metric can be extended to a full supergravity solution with non-trivial dilaton, RR scalar and RR 5-form strength. The solution depends on a free parameter a that should be chosen as a particular function of κ to correspond to the deformed supercoset model. In AdS 3 × S 3 case the full solution supported by the dilaton, RR scalar and RR 3-form strength exists only in the two special cases, a = 0 and a = 1 . We conjecture that there may be a more general one-parameter solution supported by several RR fields that for particular a = a ( κ ) corresponds to the supercoset model. In the most complicated deformed AdS 5 × S 5 case we were able to find only the expressions for the dilaton and the RR scalar. The full solution is likely to be supported by a combination of the 5-form and 3-form field strengths. We comment on the singularity structure of the resulting metric and exact dilaton field.« less

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.

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.

Neutron stars in screened modified gravity: Chameleon versus dilaton

NASA Astrophysics Data System (ADS)

Brax, Philippe; Davis, Anne-Christine; Jha, Rahul

2017-04-01

We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified gravity parameters and the neutron star equation of state. This is exemplified by the modifications to the mass-radius relationship for a variety of model parameters.

Frozen up dilaton and the GUT/Planck mass ratio

NASA Astrophysics Data System (ADS)

Davidson, Aharon; Ygael, Tomer

2017-09-01

By treating modulus and phase on equal footing, as prescribed by Dirac, local scale invariance can consistently accompany any Brans-Dicke ω-theory. We show that in the presence of a soft scale symmetry breaking term, the classical solution, if it exists, cannot be anything else but general relativistic. The dilaton modulus gets frozen up by the Weyl-Proca vector field, thereby constituting a gravitational quasi-Higgs mechanism. Assigning all grand unified scalars as dilatons, they enjoy Weyl universality, and upon symmetry breaking, the Planck (mass)2 becomes the sum of all their individual (VEV)2s. The emerging GUT/Planck (mass)2 ratio is thus ∼ ωgGUT2 / 4 π.

Phantom wormholes in Einstein–Maxwell-dilaton theory

NASA Astrophysics Data System (ADS)

Goulart, Prieslei

2018-01-01

In this paper we give an electrically charged traversable wormhole solution for the Einstein–Maxwell-dilaton theory when the dilaton is a phantom field, i.e. it has flipped sign kinetic term appearing in the action. In the limit when the charge is zero, we recover the anti-Fisher solution, which can be reduced to the Bronnikov–Ellis solution under certain choices of integration constants. The equations of motion of this theory share the same S-duality invariance of string theory, so the electrically charged solution is rotated into the magnetically charged one by applying such transformations. The scalar field is topological, so we compute its topological charge, and discuss that under appropriate boundary conditions we can have a lump, a kink, or an anti-kink profile. We determine the position of the throat, and show the embedding diagram of the wormhole. As a physical application, we apply the Gauss–Bonnet theorem to compute the deflection angle of a light-ray that passes close to the wormhole.

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

Non-singular spacetimes with a negative cosmological constant: IV. Stationary black hole solutions with matter fields

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.; Delay, Erwann; Klinger, Paul

2018-02-01

We use an elliptic system of equations with complex coefficients for a set of complex-valued tensor fields as a tool to construct infinite-dimensional families of non-singular stationary black holes, real-valued Lorentzian solutions of the Einstein–Maxwell-dilaton-scalar fields-Yang–Mills–Higgs–Chern–Simons-f(R) equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

Cosmic censorship and Weak Gravity Conjecture in the Einstein-Maxwell-dilaton theory

NASA Astrophysics Data System (ADS)

Yu, Ten-Yeh; Wen, Wen-Yu

2018-06-01

We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy. Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture.

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

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.

No hair theorem in quasi-dilaton massive gravity

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

Wu, De-Jun; Zhou, Shuang-Yong

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

No hair theorem in quasi-dilaton massive gravity

DOE PAGES

Wu, De-Jun; Zhou, Shuang-Yong

2016-04-11

We investigate the static, spherically symmetric black hole solutions in the quasi-dilaton model and its generalizations, which are scalar extended dRGT massive gravity with a shift symmetry. We show that, unlike generic scalar extended massive gravity models, these theories do not admit static, spherically symmetric black hole solutions until the theory parameters in the dRGT potential are fine-tuned. When fine-tuned, the geometry of the static, spherically symmetric black hole is necessarily that of general relativity and the quasi-dilaton field is constant across the spacetime. The fine-tuning and the no hair theorem apply to black holes with flat, anti-de Sitter ormore » de Sitter asymptotics. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).« less

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.

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.

Observing the shadow of Einstein-Maxwell-Dilaton-Axion black hole

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

Wei, Shao-Wen; Liu, Yu-Xiao, E-mail: weishw@lzu.edu.cn, E-mail: liuyx@lzu.edu.cn

In this paper, the shadows cast by Einstein-Maxwell-Dilaton-Axion black hole and naked singularity are studied. The shadow of a rotating black hole is found to be a dark zone covered by a deformed circle. For a fixed value of the spin a, the size of the shadow decreases with the dilaton parameter b. The distortion of the shadow monotonically increases with b and takes its maximal when the black hole approaches to the extremal case. Due to the optical properties, the area of the black hole shadow is supposed to equal to the high-energy absorption cross section. Based on thismore » assumption, the energy emission rate is investigated. For a naked singularity, the shadow has a dark arc and a dark spot or straight, and the corresponding observables are obtained. These results show that there is a significant effect of the spin a and dilaton parameter b on these shadows. Moreover, we examine the observables of the shadow cast by the supermassive black hole at the center of the Milky Way, which is very useful for us to probe the nature of the black hole through the astronomical observations in the near future.« less

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Collapse of charged scalar field in dilaton gravity

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

Borkowska, Anna; Rogatko, Marek; Moderski, Rafal

2011-04-15

We elaborated the gravitational collapse of a self-gravitating complex charged scalar field in the context of the low-energy limit of the string theory, the so-called dilaton gravity. We begin with the regular spacetime and follow the evolution through the formation of an apparent horizon and the final central singularity.

Asymptotic analysis of the Boltzmann equation for dark matter relics in the presence of a running dilaton and space-time defects

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Mavromatos, Nick E.; Sarkar, Sarben

2013-03-01

The interplay of dilatonic effects in dilaton cosmology and stochastic quantum space-time defects within the framework of string/brane cosmologies is examined. The Boltzmann equation describes the physics of thermal dark-matter-relic abundances in the presence of rolling dilatons. These dilatons affect the coupling of stringy matter to D-particle defects, which are generic in string theory. This coupling leads to an additional source term in the Boltzmann equation. The techniques of asymptotic matching and boundary-layer theory, which were recently applied by two of the authors (Bender and Sarkar) to a Boltzmann equation, are used here to find the detailed asymptotic relic abundances for all ranges of the expectation value of the dilaton field. The phenomenological implications for the search for supersymmetric dark matter in current colliders, such as the LHC, are discussed.

O(d,d)-duality in string theory

NASA Astrophysics Data System (ADS)

Rennecke, Felix

2014-10-01

A new method for obtaining dual string theory backgrounds is presented. Preservation of the Hamiltonian density and the energy momentum tensor induced by O( d, d)-transformations leads to a relation between dual sets of coordinate one-forms accompanied by a redefinition of the background fields and a shift of the dilaton. The necessity of isometric directions arises as integrability condition for this map. The isometry algebra is studied in detail using generalised geometry. In particular, non-abelian dualities and β-transformations are contained in this approach. The latter are exemplified by the construction of a new approximate non-geometric background.

Non-Abelian dark forces and the relic densities of dark glueballs

NASA Astrophysics Data System (ADS)

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

2017-01-01

Our understanding of the Universe is known to be incomplete, and new gauge forces beyond those of the Standard Model might be crucial to describing its observed properties. A minimal and well-motivated possibility is a pure Yang-Mills non-Abelian dark gauge force with no direct connection to the Standard Model. We determine here the relic abundances of the glueball bound states that arise in such theories and investigate their cosmological effects. Glueballs are first formed in a confining phase transition, and their relic densities are set by a network of annihilation and transfer reactions. The lightest glueball has no lighter states to annihilate into, and its yield is set mainly by 3 →2 number-changing processes which persistently release energy into the glueball gas during freeze-out. The abundances of the heavier glueballs are dominated by 2 →2 transfer reactions and tend to be much smaller than the lightest state. We also investigate potential connectors between the dark force and the Standard Model that allow some or all of the dark glueballs to decay. If the connection is weak, the lightest glueball can be very long-lived or stable and is a viable dark matter candidate. For stronger connections, the lightest glueball will decay quickly, but other heavier glueball states can remain stable and contribute to the dark matter density.

The B-field soft theorem and its unification with the graviton and dilaton

NASA Astrophysics Data System (ADS)

Di Vecchia, Paolo; Marotta, Raffaele; Mojaza, Matin

2017-10-01

In theories of Einstein gravity coupled with a dilaton and a two-form, a soft theorem for the two-form, known as the Kalb-Ramond B-field, has so far been missing. In this work we fill the gap, and in turn formulate a unified soft theorem valid for gravitons, dilatons and B-fields in any tree-level scattering amplitude involving the three massless states. The new soft theorem is fixed by means of on-shell gauge invariance and enters at the subleading order of the graviton's soft theorem. In contrast to the subsubleading soft behavior of gravitons and dilatons, we show that the soft behavior of B-fields at this order cannot be fully fixed by gauge invariance. Nevertheless, we show that it is possible to establish a gauge invariant decomposition of the amplitudes to any order in the soft expansion. We check explicitly the new soft theorem in the bosonic string and in Type II superstring theories, and furthermore demonstrate that, at the next order in the soft expansion, totally gauge invariant terms appear in both string theories which cannot be factorized into a soft theorem.

Higgs-dilaton cosmology: An inflation-dark-energy connection and forecasts for future galaxy surveys

NASA Astrophysics Data System (ADS)

Casas, Santiago; Pauly, Martin; Rubio, Javier

2018-02-01

The Higgs-dilaton model is a scale-invariant extension of the Standard Model nonminimally coupled to gravity and containing just one additional degree of freedom on top of the Standard Model particle content. This minimalistic scenario predicts a set of measurable consistency relations between the inflationary observables and the dark-energy equation-of-state parameter. We present an alternative derivation of these consistency relations that highlights the connections and differences with the α -attractor scenario. We study how far these constraints allow one to distinguish the Higgs-dilaton model from Λ CDM and w CDM cosmologies. To this end we first analyze existing data sets using a Markov chain Monte Carlo approach. Second, we perform forecasts for future galaxy surveys using a Fisher matrix approach, both for galaxy clustering and weak lensing probes. Assuming that the best fit values in the different models remain comparable to the present ones, we show that both Euclid- and SKA2-like missions will be able to discriminate a Higgs-dilaton cosmology from Λ CDM and w CDM .

General N=1 supersymmetric flux vacua of massive type IIA string theory.

PubMed

Behrndt, Klaus; Cvetic, Mirjam

2005-07-08

We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.

N = 1 supercurrents of eleven-dimensional supergravity

NASA Astrophysics Data System (ADS)

Becker, Katrin; Becker, Melanie; Butter, Daniel; Linch, William D.

2018-05-01

Eleven-dimensional supergravity can be formulated in superspaces locally of the form X × Y where X is 4D N = 1 conformal superspace and Y is an arbitrary 7-manifold admitting a G 2-structure. The eleven-dimensional 3-form and the stable 3-form on Y define the lowest component of a gauge superfield on X × Y that is chiral as a superfield on X. This chiral field is part of a tensor hierarchy giving rise to a superspace Chern-Simons action and its real field strength defines a lifting of the Hitchin functional on Y to the G 2 superspace X × Y . These terms are those of lowest order in a superspace Noether expansion in seven N = 1 conformal gravitino superfields Ψ. In this paper, we compute the O(Ψ) action to all orders in the remaining fields. The eleven-dimensional origin of the resulting non-linear structures is parameterized by the choice of a complex spinor on Y encoding the off-shell 4D N = 1 subalgebra of the eleven-dimensional super-Poincaré algebra.

Inflation from extra dimensions

NASA Astrophysics Data System (ADS)

Levin, Janna J.

1995-02-01

A gravity-driven inflation is shown to arise from a simple higher-dimensional universe. In vacuum, the shear of n > 1 contracting dimensions is able to inflate the remaining three spatial dimensions. Said another way, the expansion of the 3-volume is accelerated by the contraction of the n-volume. Upon dimensional reduction, the theory is equivalent to a four-dimensional cosmology with a dynamical Planck mass. A connection can therefore be made to recent examples of inflation powered by a dilaton kinetic energy. Unfortunately, the graceful exit problem encountered in dilaton cosmologies will haunt this cosmology as well.

Hidden SU ( N ) glueball dark matter

DOE PAGES

Soni, Amarjit; Zhang, Yue

2016-06-21

Here we investigate the possibility that the dark matter candidate is from a pure non-abelian gauge theory of the hidden sector, motivated in large part by its elegance and simplicity. The dark matter is the lightest bound state made of the confined gauge fields, the hidden glueball. We point out this simple setup is capable of providing rich and novel phenomena in the dark sector, especially in the parameter space of large N. They include self-interacting and warm dark matter scenarios, Bose-Einstein condensation leading to massive dark stars possibly millions of times heavier than our sun giving rise to gravitationalmore » lensing effects, and indirect detections through higher dimensional operators as well as interesting collider signatures.« less

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.

Holographic Techni-Dilaton, or Conformal Higgs

NASA Astrophysics Data System (ADS)

Habaa, Kazumoto; Matsuzaki, Shinya; Yamawaki, Koichi

2011-01-01

We study a holographic model dual to walking/conformal technicolor (W/C TC) deforming a hard-wall type of bottom-up setup by including effects from techni-gluon condensation. We calculate masses of (techni-) ρ meson, a1 meson, and flavor/chiral-singlet scalar meson identified with techni-dilaton (TD)/conformal Higgs boson, as well as the S parameter. It is shown that gluon contributions and large anomalous dimension tend to decrease specifically mass of the TD. In the typical model with S ≃ 0.1, we find mTD ≃ 600 GeV, while mρ, ma1 ≃ 4TeV.

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

All Chern-Simons invariants of 4D, N = 1 gauged superform hierarchies

NASA Astrophysics Data System (ADS)

Becker, Katrin; Becker, Melanie; Linch, William D.; Randall, Stephen; Robbins, Daniel

2017-04-01

We give a geometric description of supersymmetric gravity/(non-)abelian p-form hierarchies in superspaces with 4D, N = 1 super-Poincaré invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, N = 1 graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/ BF -type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of p-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF -type and cubic Chern-Simons actions. As an application, we compute the quartic invariant ˜ AdAdAdA + . . . relevant, for example, to seven-dimensional supergravity compactifications.

Two-dimensional chiral topological superconductivity in Shiba lattices

PubMed Central

Li, Jian; Neupert, Titus; Wang, Zhijun; MacDonald, A. H.; Yazdani, A.; Bernevig, B. Andrei

2016-01-01

The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal. PMID:27465127

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.

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.

The effective supergravity of little string theory

NASA Astrophysics Data System (ADS)

Antoniadis, Ignatios; Delgado, Antonio; Markou, Chrysoula; Pokorski, Stefan

2018-02-01

In this work we present the minimal supersymmetric extension of the five-dimensional dilaton-gravity theory that captures the main properties of the holographic dual of little string theory. It is described by a particular gauging of N=2 supergravity coupled with one vector multiplet associated with the string dilaton, along the U(1) subgroup of SU(2) R-symmetry. The linear dilaton in the fifth coordinate solution of the equations of motion (with flat string frame metric) breaks half of the supersymmetries to N=1 in four dimensions. Interest in the linear dilaton model has lately been revived in the context of the clockwork mechanism, which has recently been proposed as a new source of exponential scale separation in field theory.

Non-locality of non-Abelian anyons

NASA Astrophysics Data System (ADS)

Brennen, G. K.; Iblisdir, S.; Pachos, J. K.; Slingerland, J. K.

2009-10-01

Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.

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].

Symmetry breaking patterns for inflation

NASA Astrophysics Data System (ADS)

Klein, Remko; Roest, Diederik; Stefanyszyn, David

2018-06-01

We study inflationary models where the kinetic sector of the theory has a non-linearly realised symmetry which is broken by the inflationary potential. We distinguish between kinetic symmetries which non-linearly realise an internal or space-time group, and which yield a flat or curved scalar manifold. This classification leads to well-known inflationary models such as monomial inflation and α-attractors, as well as a new model based on fixed couplings between a dilaton and many axions which non-linearly realises higher-dimensional conformal symmetries. In this model, inflation can be realised along the dilatonic direction, leading to a tensor-to-scalar ratio r ˜ 0 .01 and a spectral index n s ˜ 0 .975. We refer to the new model as ambient inflation since inflation proceeds along an isometry of an anti-de Sitter ambient space-time, which fully determines the kinetic sector.

Quasi-one-dimensional quantum anomalous Hall systems as new platforms for scalable topological quantum computation

NASA Astrophysics Data System (ADS)

Chen, Chui-Zhen; Xie, Ying-Ming; Liu, Jie; Lee, Patrick A.; Law, K. T.

2018-03-01

Quantum anomalous Hall insulator/superconductor heterostructures emerged as a competitive platform to realize topological superconductors with chiral Majorana edge states as shown in recent experiments [He et al. Science 357, 294 (2017), 10.1126/science.aag2792]. However, chiral Majorana modes, being extended, cannot be used for topological quantum computation. In this work, we show that quasi-one-dimensional quantum anomalous Hall structures exhibit a large topological regime (much larger than the two-dimensional case) which supports localized Majorana zero energy modes. The non-Abelian properties of a cross-shaped quantum anomalous Hall junction is shown explicitly by time-dependent calculations. We believe that the proposed quasi-one-dimensional quantum anomalous Hall structures can be easily fabricated for scalable topological quantum computation.

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.

A four-dimensional model with the fermionic determinant exactly evaluated

NASA Astrophysics Data System (ADS)

Mignaco, J. A.; Rego Monteiro, M. A.

1986-07-01

A method is presented to compute the fermion determinant of some class of field theories. By this method the following results of the fermion determinant in two dimensions are easily recovered: (i) Schwinger model without reference to a particular gauge. (ii) QCD in the light-cone gauge. (iii) Gauge invariant result of QCD. The method is finally applied to give an analytical solution of the fermion determinant of a four-dimensional, non-abelian, Dirac-like theory with massless fermions interacting with an external vector field through a pseudo-vectorial coupling. Fellow of the Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil.

Fermions tunneling from the Horowitz-Strominger Dilaton black hole

NASA Astrophysics Data System (ADS)

Li, Qiang; Zeng, Xiaoxiong

2009-06-01

Based on the work of Kerner and Mann, fermions tunneling from the Horowitz-Strominger Dilaton black hole on the membrane is studied. Owing to the coupling among electromagnetic field, matter field and gravity field, the Dirac equation of charged particles is introduced, and according to that, the expected emission temperature is obtained. After the self-gravitational interaction is considered, it is found that the tunneling rate of fermions also satisfies the underlying Unitary theory as the case of scalar particles.

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.

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.

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.

Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.

PubMed

Diakonos, F K; Katsimiga, G C; Maintas, X N; Tsagkarakis, C E

2015-02-01

We study the classical dynamics of the Abelian-Higgs model in (1 + 1) space-time dimensions for the case of strongly broken gauge symmetry. In this limit the wells of the potential are almost harmonic and sufficiently deep, presenting a scenario far from the associated critical point. Using a multiscale perturbation expansion, the equations of motion for the fields are reduced to a system of coupled nonlinear Schrödinger equations. Exact solutions of the latter are used to obtain approximate analytical solutions for the full dynamics of both the gauge and Higgs field in the form of oscillons and oscillating kinks. Numerical simulations of the exact dynamics verify the validity of these solutions. We explore their persistence for a wide range of the model's single parameter, which is the ratio of the Higgs mass (m(H)) to the gauge-field mass (m(A)). We show that only oscillons oscillating symmetrically with respect to the "classical vacuum," for both the gauge and the Higgs field, are long lived. Furthermore, plane waves and oscillating kinks are shown to decay into oscillon-like patterns, due to the modulation instability mechanism.

Fractal electrodynamics via non-integer dimensional space approach

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

S-duality constraint on higher-derivative couplings

NASA Astrophysics Data System (ADS)

Garousi, Mohammad R.

2014-05-01

The Riemann curvature correction to the type II supergravity at eightderivative level in string frame is given as . For constant dilaton, it has been extended in the literature to the S-duality invariant form by extending the dilaton factor in the Einstein frame to the non-holomorphic Eisenstein series. For non-constant dilaton, however, there are various couplings in the Einstein frame which are not consistent with the S-duality. By constructing the tensors t 2 n from Born-Infeld action, we include the appropriate Ricci and scalar curvatures as well as the dilaton couplings to make the above action to be consistent with the S-duality.

Comprehensive non-dimensional normalization of gait data.

PubMed

Pinzone, Ornella; Schwartz, Michael H; Baker, Richard

2016-02-01

Normalizing clinical gait analysis data is required to remove variability due to physical characteristics such as leg length and weight. This is particularly important for children where both are associated with age. In most clinical centres conventional normalization (by mass only) is used whereas there is a stronger biomechanical argument for non-dimensional normalization. This study used data from 82 typically developing children to compare how the two schemes performed over a wide range of temporal-spatial and kinetic parameters by calculating the coefficients of determination with leg length, weight and height. 81% of the conventionally normalized parameters had a coefficient of determination above the threshold for a statistical association (p<0.05) compared to 23% of those normalized non-dimensionally. All the conventionally normalized parameters exceeding this threshold showed a reduced association with non-dimensional normalization. In conclusion, non-dimensional normalization is more effective that conventional normalization in reducing the effects of height, weight and age in a comprehensive range of temporal-spatial and kinetic parameters. Copyright © 2015 Elsevier B.V. All rights reserved.

Quantization of a theory of 2D dilaton gravity

NASA Astrophysics Data System (ADS)

de Alwis, S. P.

1992-09-01

We discuss the quantization of the 2D gravity theory of Callan, Giddings, Harvey, and Strominger (CGHS), following the procedure of David, and of Distler and Kawai. We find that the physics depends crucially on whether the number of matter fields is greater than or less than 24. In the latter case the singularity pointed out by several authors is absent but the physical interpretation is unclear. In the former case (the one studied by CGHS) the quantum theory which gives CGHS in the linear dilaton semi-classical limit, is different from that which gives CGHS in the extreme Liouville regime.

Exponents of non-linear clustering in scale-free one-dimensional cosmological simulations

NASA Astrophysics Data System (ADS)

Benhaiem, David; Joyce, Michael; Sicard, François

2013-03-01

One-dimensional versions of dissipationless cosmological N-body simulations have been shown to share many qualitative behaviours of the three-dimensional problem. Their interest lies in the fact that they can resolve a much greater range of time and length scales, and admit exact numerical integration. We use such models here to study how non-linear clustering depends on initial conditions and cosmology. More specifically, we consider a family of models which, like the three-dimensional Einstein-de Sitter (EdS) model, lead for power-law initial conditions to self-similar clustering characterized in the strongly non-linear regime by power-law behaviour of the two-point correlation function. We study how the corresponding exponent γ depends on the initial conditions, characterized by the exponent n of the power spectrum of initial fluctuations, and on a single parameter κ controlling the rate of expansion. The space of initial conditions/cosmology divides very clearly into two parts: (1) a region in which γ depends strongly on both n and κ and where it agrees very well with a simple generalization of the so-called stable clustering hypothesis in three dimensions; and (2) a region in which γ is more or less independent of both the spectrum and the expansion of the universe. The boundary in (n, κ) space dividing the `stable clustering' region from the `universal' region is very well approximated by a `critical' value of the predicted stable clustering exponent itself. We explain how this division of the (n, κ) space can be understood as a simple physical criterion which might indeed be expected to control the validity of the stable clustering hypothesis. We compare and contrast our findings to results in three dimensions, and discuss in particular the light they may throw on the question of `universality' of non-linear clustering in this context.

Lectures on Non-Abelian Bosonization

NASA Astrophysics Data System (ADS)

Tsvelik, A. M.

The following sections are included: * Introduction * Kac-Moody algebra * Conformal embedding. Sugawara Hamiltonian * SU(N)×SU(M) model * From the fermionic to WZNW model * The perturbed SUk(2) WZNW model * Correlation functions and Quasi Long Range order * Generalization from SU(2) to SU(N) * A model with Sp(2N) symmetry * Solution for the special case gcdw = gsc * Attraction in the orbital channel. Competing orders. Emergent integrability. ZN parafermions. * Parafermion zero modes * Conclusions and Acknowledgements * Appendix A. TBA equations for the Sp1(2N) model * Appendix B. Bosonization of of Z4 parafermions * References

Ultra-weak sector, Higgs boson mass, and the dilaton

DOE PAGES

Allison, Kyle; Hill, Christopher T.; Ross, Graham G.

2014-09-26

The Higgs boson mass may arise from a portal coupling to a singlet fieldmore » $$\\sigma$$ which has a very large VEV $$f \\gg m_\\text{Higgs}$$. This requires a sector of "ultra-weak" couplings $$\\zeta_i$$, where $$\\zeta_i \\lesssim m_\\text{Higgs}^2 / f^2$$. Ultra-weak couplings are technically naturally small due to a custodial shift symmetry of $$\\sigma$$ in the $$\\zeta_i \\rightarrow 0$$ limit. The singlet field $$\\sigma$$ has properties similar to a pseudo-dilaton. We engineer explicit breaking of scale invariance in the ultra-weak sector via a Coleman-Weinberg potential, which requires hierarchies amongst the ultra-weak couplings.« less

Baryon asymmetry from hypermagnetic helicity in dilaton hypercharge electromagnetism

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

Bamba, Kazuharu

2006-12-15

The generation of the baryon asymmetry of the Universe from the hypermagnetic helicity, the physical interpretation of which is given in terms of hypermagnetic knots, is studied in inflationary cosmology, taking into account the breaking of the conformal invariance of hypercharge electromagnetic fields through both a coupling with the dilaton and with a pseudoscalar field. It is shown that, if the electroweak phase transition is strongly first order and the present amplitude of the generated magnetic fields on the horizon scale is sufficiently large, a baryon asymmetry with a sufficient magnitude to account for the observed baryon-to-entropy ratio can bemore » generated.« less

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.

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

On spacetime structure and electrodynamics

NASA Astrophysics Data System (ADS)

Ni, Wei-Tou

2016-10-01

Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell-Lorentz electrodynamics. Introducing the metric gij as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the

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.

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.

Entropy of a (1+1)-dimensional charged black hole to all orders in the Planck length

NASA Astrophysics Data System (ADS)

Kim, Yong-Wan; Park, Young-Jai

2013-02-01

We study the statistical entropy of a scalar field on the (1+1)-dimensional Maxwell-dilaton background without an artificial cutoff by considering corrections to all orders in the Planck length obtained from a generalized uncertainty principle applied to the quantum state density. In contrast to the previous results for d ≥ 3 dimensional cases, we obtain an unadjustable entropy due to the independence of the minimal length, which plays the role of an adjustable parameter. However, this entropy is still proportional to the Bekenstein-Hawking entropy.

The edge of supersymmetry: Stability walls in heterotic theory

DOE PAGES

Anderson, Lara B.; Gray, James; Lukas, Andre; ...

2009-05-15

We explicitly describe, in the language of four-dimensional N = 1 supersymmetric field theory, what happens when the moduli of a heterotic Calabi-Yau compactification change so as to make the internal non-Abelian gauge fields non-supersymmetric. At the edge of the region in Kähler moduli space where supersymmetry can be preserved, an additional anomalous U(1) gauge symmetry appears in the four-dimensional theory. The D-term contribution to the scalar potential associated to this U(1) attempts to force the system back into a supersymmetric configuration and provides a consistent low-energy description of gauge bundle stability.

Dilatonic BTZ black holes with power-law field

NASA Astrophysics Data System (ADS)

Hendi, S. H.; Eslam Panah, B.; Panahiyan, S.; Sheykhi, A.

2017-04-01

Motivated by low energy effective action of string theory and numerous applications of BTZ black holes, we will consider minimal coupling between dilaton and nonlinear electromagnetic fields in three dimensions. The main goal is studying thermodynamical structure of black holes in this set up. Temperature and heat capacity of these black holes are investigated and a picture regarding their phase transitions is given. In addition, the role and importance of studying the mass of black holes is highlighted. We will see how different parameters modify thermodynamical quantities, hence thermodynamical structure of these black holes. In addition, geometrical thermodynamics is used to investigate thermodynamical properties of these black holes. In this regard, the successful method is presented and the nature of interaction around bound and phase transition points is studied.

n-SIFT: n-dimensional scale invariant feature transform.

PubMed

Cheung, Warren; Hamarneh, Ghassan

2009-09-01

We propose the n-dimensional scale invariant feature transform (n-SIFT) method for extracting and matching salient features from scalar images of arbitrary dimensionality, and compare this method's performance to other related features. The proposed features extend the concepts used for 2-D scalar images in the computer vision SIFT technique for extracting and matching distinctive scale invariant features. We apply the features to images of arbitrary dimensionality through the use of hyperspherical coordinates for gradients and multidimensional histograms to create the feature vectors. We analyze the performance of a fully automated multimodal medical image matching technique based on these features, and successfully apply the technique to determine accurate feature point correspondence between pairs of 3-D MRI images and dynamic 3D + time CT data.

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

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

Multipoint correlators in the Abelian sandpile model

NASA Astrophysics Data System (ADS)

Poncelet, Adrien; Ruelle, Philippe

2017-12-01

We revisit the calculation of height correlations in the two-dimensional Abelian sandpile model by taking advantage of a technique developed recently by Kenyon and Wilson. The formalism requires to equip the usual graph Laplacian, ubiquitous in the context of cycle-rooted spanning forests, with a complex connection. In the case at hand, the connection is constant and localized along a semi-infinite defect line (zipper). In the appropriate limit of a trivial connection, it allows one to count spanning forests whose components contain prescribed sites, which are of direct relevance for height correlations in the sandpile model. Using this technique, we first rederive known 1- and 2-site lattice correlators on the plane and upper half-plane, more efficiently than what has been done so far. We also compute explicitly the (new) next-to-leading order in the distances (r-4 for 1-site on the upper half-plane, r-6 for 2-site on the plane). We extend these results by computing new correlators involving one arbitrary height and a few heights 1 on the plane and upper half-plane, for the open and closed boundary conditions. We examine our lattice results from the conformal point of view, and confirm the full consistency with the specific features currently conjectured to be present in the associated logarithmic conformal field theory.

Implementing odd-axions in dimensional oxidation of 4D non-geometric type IIB scalar potential

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2016-01-01

In a setup of type IIB superstring compactification on an orientifold of a T6 /Z4 sixfold, the presence of geometric flux (ω) and non-geometric fluxes (Q, R) is implemented along with the standard NS-NS and RR three-form fluxes (H, F). After computing the F/D-term contributions to the N = 1 four dimensional effective scalar potential, we rearrange the same into 'suitable' pieces by using a set of new generalized flux orbits. Subsequently, we dimensionally oxidize the various pieces of the total four dimensional scalar potential to guess their ten-dimensional origin.

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.

The Law of Cosines for an "n"-Dimensional Simplex

ERIC Educational Resources Information Center

Ding, Yiren

2008-01-01

Using the divergence theorem technique of L. Eifler and N.H. Rhee, "The n-dimensional Pythagorean Theorem via the Divergence Theorem" (to appear: Amer. Math. Monthly), we extend the law of cosines for a triangle in a plane to an "n"-dimensional simplex in an "n"-dimensional space.

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.

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

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.

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.

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.

High-dimensional Controlled-phase Gate Between a 2 N -dimensional Photon and N Three-level Artificial Atoms

NASA Astrophysics Data System (ADS)

Ma, Yun-Ming; Wang, Tie-Jun

2017-10-01

Higher-dimensional quantum system is of great interest owing to the outstanding features exhibited in the implementation of novel fundamental tests of nature and application in various quantum information tasks. High-dimensional quantum logic gate is a key element in scalable quantum computation and quantum communication. In this paper, we propose a scheme to implement a controlled-phase gate between a 2 N -dimensional photon and N three-level artificial atoms. This high-dimensional controlled-phase gate can serve as crucial components of the high-capacity, long-distance quantum communication. We use the high-dimensional Bell state analysis as an example to show the application of this device. Estimates on the system requirements indicate that our protocol is realizable with existing or near-further technologies. This scheme is ideally suited to solid-state integrated optical approaches to quantum information processing, and it can be applied to various system, such as superconducting qubits coupled to a resonator or nitrogen-vacancy centers coupled to a photonic-band-gap structures.

On the motion of hairy black holes in Einstein-Maxwell-dilaton theories

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis

2018-01-01

Starting from the static, spherically symmetric black hole solutions in massless Einstein-Maxwell-dilaton (EMD) theories, we build a "skeleton" action, that is, we phenomenologically replace black holes by an appropriate effective point particle action, which is well suited to the formal treatment of the many-body problem in EMD theories. We find that, depending crucially on the value of their scalar cosmological environment, black holes can undergo steep "scalarization" transitions, inducing large deviations to the general relativistic two-body dynamics, as shown, for example, when computing the first post-Keplerian Lagrangian of EMD theories.

Chameleonic dilaton, nonequivalent frames, and the cosmological constant problem in quantum string theory

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

Zanzi, Andrea

2010-08-15

The chameleonic behavior of the string theory dilaton is suggested. Some of the possible consequences of the chameleonic string dilaton are analyzed in detail. In particular, (1) we suggest a new stringy solution to the cosmological constant problem and (2) we point out the nonequivalence of different conformal frames at the quantum level. In order to obtain these results, we start taking into account the (strong coupling) string loop expansion in the string frame (S-frame), therefore the so-called form factors are present in the effective action. The correct dark energy scale is recovered in the Einstein frame (E-frame) without unnaturalmore » fine-tunings and this result is robust against all quantum corrections, granted that we assume a proper structure of the S-frame form factors in the strong coupling regime. At this stage, the possibility still exists that a certain amount of fine-tuning may be required to satisfy some phenomenological constraints. Moreover in the E-frame, in our proposal, all the interactions are switched off on cosmological length scales (i.e., the theory is IR-free), while higher derivative gravitational terms might be present locally (on short distances) and it remains to be seen whether these facts clash with phenomenology. A detailed phenomenological analysis is definitely necessary to clarify these points.« less

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

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).

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.

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.

New Results in {mathcal {N}}=2 N = 2 Theories from Non-perturbative String

NASA Astrophysics Data System (ADS)

Bonelli, Giulio; Grassi, Alba; Tanzini, Alessandro

2018-03-01

We describe the magnetic phase of SU(N) $\\mathcal{N}=2$ Super Yang-Mills theories in the self-dual Omega background in terms of a new class of multi-cut matrix models. These arise from a non-perturbative completion of topological strings in the dual four dimensional limit which engineers the gauge theory in the strongly coupled magnetic frame. The corresponding spectral determinants provide natural candidates for the tau functions of isomonodromy problems for flat spectral connections associated to the Seiberg-Witten geometry.

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.

On whole Abelian model dynamics

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

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

2012-09-24

Physics challenge is to determine the objects dynamics. However, there are two ways for deciphering the part. The first one is to search for the ultimate constituents; the second one is to understand its behaviour in whole terms. Therefore, the parts can be defined either from elementary constituents or as whole functions. Historically, science has been moving through the first aspect, however, quarks confinement and complexity are interrupting this usual approach. These relevant facts are supporting for a systemic vision be introduced. Our effort here is to study on the whole meaning through gauge theory. Consider a systemic dynamics orientedmore » through the U(1) - systemic gauge parameter which function is to collect a fields set {l_brace}A{sub {mu}I}{r_brace}. Derive the corresponding whole gauge invariant Lagrangian, equations of motion, Bianchi identities, Noether relationships, charges and Ward-Takahashi equations. Whole Lorentz force and BRST symmetry are also studied. These expressions bring new interpretations further than the usual abelian model. They are generating a systemic system governed by 2N+ 10 classical equations plus Ward-Takahashi identities. A whole dynamics based on the notions of directive and circumstance is producing a set determinism where the parts dynamics are inserted in the whole evolution. A dynamics based on state, collective and individual equations with a systemic interdependence.« less

Non-dimensional physics of pulsatile cardiovascular networks and energy efficiency.

PubMed

Yigit, Berk; Pekkan, Kerem

2016-01-01

In Nature, there exist a variety of cardiovascular circulation networks in which the energetic ventricular load has both steady and pulsatile components. Steady load is related to the mean cardiac output (CO) and the haemodynamic resistance of the peripheral vascular system. On the other hand, the pulsatile load is determined by the simultaneous pressure and flow waveforms at the ventricular outlet, which in turn are governed through arterial wave dynamics (transmission) and pulse decay characteristics (windkessel effect). Both the steady and pulsatile contributions of the haemodynamic power load are critical for characterizing/comparing disease states and for predicting the performance of cardiovascular devices. However, haemodynamic performance parameters vary significantly from subject to subject because of body size, heart rate and subject-specific CO. Therefore, a 'normalized' energy dissipation index, as a function of the 'non-dimensional' physical parameters that govern the circulation networks, is needed for comparative/integrative biological studies and clinical decision-making. In this paper, a complete network-independent non-dimensional formulation that incorporates pulsatile flow regimes is developed. Mechanical design variables of cardiovascular flow systems are identified and the Buckingham Pi theorem is formally applied to obtain the corresponding non-dimensional scaling parameter sets. Two scaling approaches are considered to address both the lumped parameter networks and the distributed circulation components. The validity of these non-dimensional number sets is tested extensively through the existing empirical allometric scaling laws of circulation systems. Additional validation studies are performed using a parametric numerical arterial model that represents the transmission and windkessel characteristics, which are adjusted to represent different body sizes and non-dimensional haemodynamic states. Simulations demonstrate that the proposed non-dimensional

Extrema of mass, first law of black hole mechanics, and a staticity theorem in Einstein-Maxwell-axion-dilaton gravity

NASA Astrophysics Data System (ADS)

Rogatko, Marek

1998-08-01

Using the ADM formulation of the Einstein-Maxwell axion-dilaton gravity we derive the formulas for the variation of mass and other asymptotic conserved quantities in the theory under consideration. Generalizing this kind of reasoning to the initial data for the manifold with an interior boundary we get the generalized first law of black hole mechanics. We consider an asymptotically flat solution to the Einstein-Maxwell axion-dilaton gravity describing a black hole with a Killing vector field timelike at infinity, the horizon of which comprises a bifurcate Killing horizon with a bifurcate surface. Supposing that the Killing vector field is asymptotically orthogonal to the static hypersurface with boundary S and a compact interior, we find that the solution is static in the exterior world, when the timelike vector field is normal to the horizon and has vanishing electric and axion-electric fields on static slices.

MICROSCOPE Mission: First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton

NASA Astrophysics Data System (ADS)

Bergé, Joel; Brax, Philippe; Métris, Gilles; Pernot-Borràs, Martin; Touboul, Pierre; Uzan, Jean-Philippe

2018-04-01

The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the Eötvös parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than 10-12 eV (i.e., range larger than a few 1 05 m ), we improve existing constraints by one order of magnitude to |α |<10-11 if the scalar field couples to the baryon number and to |α |<10-12 if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: We find that, for masses smaller than 10-12 eV , the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests.

MICROSCOPE Mission: First Constraints on the Violation of the Weak Equivalence Principle by a Light Scalar Dilaton.

PubMed

Bergé, Joel; Brax, Philippe; Métris, Gilles; Pernot-Borràs, Martin; Touboul, Pierre; Uzan, Jean-Philippe

2018-04-06

The existence of a light or massive scalar field with a coupling to matter weaker than gravitational strength is a possible source of violation of the weak equivalence principle. We use the first results on the Eötvös parameter by the MICROSCOPE experiment to set new constraints on such scalar fields. For a massive scalar field of mass smaller than 10^{-12}  eV (i.e., range larger than a few 10^{5}  m), we improve existing constraints by one order of magnitude to |α|<10^{-11} if the scalar field couples to the baryon number and to |α|<10^{-12} if the scalar field couples to the difference between the baryon and the lepton numbers. We also consider a model describing the coupling of a generic dilaton to the standard matter fields with five parameters, for a light field: We find that, for masses smaller than 10^{-12}  eV, the constraints on the dilaton coupling parameters are improved by one order of magnitude compared to previous equivalence principle tests.

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.

Synthesis of two-dimensional titanium nitride Ti4N3 (MXene)

NASA Astrophysics Data System (ADS)

Urbankowski, Patrick; Anasori, Babak; Makaryan, Taron; Er, Dequan; Kota, Sankalp; Walsh, Patrick L.; Zhao, Mengqiang; Shenoy, Vivek B.; Barsoum, Michel W.; Gogotsi, Yury

2016-06-01

We report on the synthesis of the first two-dimensional transition metal nitride, Ti4N3-based MXene. In contrast to the previously reported MXene synthesis methods - in which selective etching of a MAX phase precursor occurred in aqueous acidic solutions - here a molten fluoride salt is used to etch Al from a Ti4AlN3 powder precursor at 550 °C under an argon atmosphere. We further delaminated the resulting MXene to produce few-layered nanosheets and monolayers of Ti4N3Tx, where T is a surface termination (F, O, or OH). Density functional theory calculations of bare, non-terminated Ti4N3 and terminated Ti4N3Tx were performed to determine the most energetically stable form of this MXene. Bare and functionalized Ti4N3 are predicted to be metallic. Bare Ti4N3 is expected to show magnetism, which is significantly reduced in the presence of functional groups.We report on the synthesis of the first two-dimensional transition metal nitride, Ti4N3-based MXene. In contrast to the previously reported MXene synthesis methods - in which selective etching of a MAX phase precursor occurred in aqueous acidic solutions - here a molten fluoride salt is used to etch Al from a Ti4AlN3 powder precursor at 550 °C under an argon atmosphere. We further delaminated the resulting MXene to produce few-layered nanosheets and monolayers of Ti4N3Tx, where T is a surface termination (F, O, or OH). Density functional theory calculations of bare, non-terminated Ti4N3 and terminated Ti4N3Tx were performed to determine the most energetically stable form of this MXene. Bare and functionalized Ti4N3 are predicted to be metallic. Bare Ti4N3 is expected to show magnetism, which is significantly reduced in the presence of functional groups. Electronic supplementary information (ESI) available. See DOI: 10.1039/c6nr02253g

IIB duals of D = 3 {N} = 4 circular quivers

NASA Astrophysics Data System (ADS)

Assel, Benjamin; Bachas, Costas; Estes, John; Gomis, Jaume

2012-12-01

We construct the type-IIB AdS4 ⋉ K supergravity solutions which are dual to the three-dimensional {N} = 4 superconformal field theories that arise as infrared fixed points of circular-quiver gauge theories. These superconformal field theories are labeled by a triple ( {ρ, hat{ρ},L} ) subject to constraints, where ρ and hat{ρ} are two partitions of a number N, and L is a positive integer. We show that in the limit of large L the localized five- branes in our solutions are effectively smeared, and these type-IIB solutions are dual to the near-horizon geometry of M-theory M2-branes at a {{{{{{C}}^4}}} / {{( {{Z_k}× {Z_{widehat{k}}}} )}} .} orbifold singularity. Our IIB solutions resolve the singularity into localized five-brane throats, without breaking the conformal symmetry. The constraints satisfied by the triple ( {ρ, hat{ρ},L} ) , together with the enhanced non-abelian flavour symmetries of the superconformal field theories are precisely reproduced by the type-IIB supergravity solutions. As a bonus, we uncover a novel type of "orbifold equivalence" between different quantum field theories and provide quantitative evidence for this equivalence.

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

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.

Signatures of Higgs dilaton and critical Higgs inflation.

PubMed

García-Bellido, Juan

2018-03-06

We test the Higgs dilaton inflation model (HDM) using the latest cosmological datasets, including the cosmic microwave background temperature, polarization and lensing data from the Planck satellite (2015), the BICEP and Keck Array experiments, the type Ia supernovae from the JLA catalogue, the baryon acoustic oscillations from CMASS, LOWZ and 6dF, the weak lensing data from the CFHTLenS survey and the matter power spectrum measurements from the latest SDSS data release. We find that the values of all cosmological parameters allowed by the HDM are well within the Planck satellite (2015) constraints. In particular, we determine [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] (at 95.5% c.l.). We also place new stringent constraints on the couplings of the HDM, ξ χ <0.00328 and [Formula: see text] (at 95.5% c.l.). We find that the HDM is only slightly better than the w 0 w a CDM model, with [Formula: see text] Given that the HDM has two fewer parameters, we find Bayesian evidence favouring the HDM over the w 0 w a CDM model. We also study the critical Higgs inflation model, taking into account the running of both the self-coupling λ( μ ) and the non-minimal coupling to gravity ξ ( μ ). We find peaks in the curvature power spectrum at scales corresponding to the critical value μ that re-enter during the radiation era and collapse to form a broad distribution of clustered primordial black holes, which could constitute today the main component of dark matter.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).

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.

On the Decay of Correlations in Non-Analytic SO(n)-Symmetric Models

NASA Astrophysics Data System (ADS)

Naddaf, Ali

We extend the method of complex translations which was originally employed by McBryan-Spencer [2] to obtain a decay rate for the two point function in two-dimensional SO(n)-symmetric models with non-analytic Hamiltonians for $.

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

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.

Consistent compactification of double field theory on non-geometric flux backgrounds

NASA Astrophysics Data System (ADS)

Hassler, Falk; Lüst, Dieter

2014-05-01

In this paper, we construct non-trivial solutions to the 2 D-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies 2( D - d) internal directions with a twist U M N which is directly connected to the covariant fluxes ABC . It exhibits 2( D - d) linear independent generalized Killing vectors K I J and gives rise to a gauged supergravity in d dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For ( D - d) = 3 we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

On the intersection of irreducible components of the space of finite-dimensional Lie algebras

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

Gorbatsevich, Vladimir V

2012-07-31

The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra ismore » considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.« less

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.

Methods, apparatuses, and computer-readable media for projectional morphological analysis of N-dimensional signals

DOEpatents

Glazoff, Michael V.; Gering, Kevin L.; Garnier, John E.; Rashkeev, Sergey N.; Pyt'ev, Yuri Petrovich

2016-05-17

Embodiments discussed herein in the form of methods, systems, and computer-readable media deal with the application of advanced "projectional" morphological algorithms for solving a broad range of problems. In a method of performing projectional morphological analysis, an N-dimensional input signal is supplied. At least one N-dimensional form indicative of at least one feature in the N-dimensional input signal is identified. The N-dimensional input signal is filtered relative to the at least one N-dimensional form and an N-dimensional output signal is generated indicating results of the filtering at least as differences in the N-dimensional input signal relative to the at least one N-dimensional form.

Constraint analysis of two-dimensional quadratic gravity from { BF} theory

NASA Astrophysics Data System (ADS)

Valcárcel, C. E.

2017-01-01

Quadratic gravity in two dimensions can be formulated as a background field ( BF) theory plus an interaction term which is polynomial in both, the gauge and background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions. In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.

Power law of shear viscosity in Einstein-Maxwell-Dilaton-Axion model

NASA Astrophysics Data System (ADS)

Ling, Yi; Xian, Zhuoyu; Zhou, Zhenhua

2017-02-01

We construct charged black hole solutions with hyperscaling violation in the infrared (IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ˜ T κ , where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current. Supported by National Natural Science Foundation of China (11275208, 11575195), Opening Project of Shanghai Key Laboratory of High Temperature Superconductors (14DZ2260700) and Jiangxi Young Scientists (JingGang Star) Program and 555 Talent Project of Jiangxi Province

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

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.

Vector calculus in non-integer dimensional space and its applications to fractal media

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Late-time evolution of a self-interacting scalar field in the spacetime of a dilaton black hole

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

Moderski, Rafal; Rogatko, Marek

2001-08-15

We investigate the late-time tails of self-interacting (massive) scalar fields in the spacetime of a dilaton black hole. Following the no hair theorem we examine the mechanism by which self-interacting scalar hair decays. We reveal that the intermediate asymptotic behavior of the considered field perturbations is dominated by an oscillatory inverse power-law decaying tail. The numerical simulations show that at very late time, massive self-interacting scalar hair decays slower than any power law.

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.

Lifshitz black branes and DC transport coefficients in massive Einstein-Maxwell-dilaton gravity

NASA Astrophysics Data System (ADS)

Kuang, Xiao-Mei; Papantonopoulos, Eleftherios; Wu, Jian-Pin; Zhou, Zhenhua

2018-03-01

We construct analytical Lifshitz massive black brane solutions in massive Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of these black brane solutions and obtain the thermodynamical stability conditions. On the dual nonrelativistic boundary field theory with Lifshitz symmetry, we analytically compute the DC transport coefficients, including the electric conductivity, thermoelectric conductivity, and thermal conductivity. The novel property of our model is that the massive term supports the Lifshitz black brane solutions with z ≠1 in such a way that the DC transport coefficients in the dual field theory are finite. We also find that the Wiedemann-Franz law in this dual boundary field theory is violated, which indicates that it may involve strong interactions.

Three-Dimensional Non-Fermi-Liquid Behavior from One-Dimensional Quantum Critical Local Moments

DOE PAGES

Classen, Laura; Zaliznyak, Igor; Tsvelik, Alexei M.

2018-04-10

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb 2Pt 2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the twomore » interacting subsystems. Lastly, we characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.« less

Three-Dimensional Non-Fermi-Liquid Behavior from One-Dimensional Quantum Critical Local Moments

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

Classen, Laura; Zaliznyak, Igor; Tsvelik, Alexei M.

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb 2Pt 2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the twomore » interacting subsystems. Lastly, we characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.« less

Three-Dimensional Non-Fermi-Liquid Behavior from One-Dimensional Quantum Critical Local Moments

NASA Astrophysics Data System (ADS)

Classen, Laura; Zaliznyak, Igor; Tsvelik, Alexei M.

2018-04-01

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three-dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb2 Pt2 Pb , a metal where itinerant electrons coexist with localized moments of Yb ions which can be described in terms of effective S =1 /2 spins with a dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the two interacting subsystems. We characterize the corresponding non-Fermi liquid behavior due to the spin criticality by calculating the electronic relaxation rate and the dc resistivity and establish its quasilinear temperature dependence.

Dimensional Transmutation by Monopole Condensation in QCD

NASA Astrophysics Data System (ADS)

Cho, Y. M.

2015-01-01

The dimensional transmutation by the monopole condensation in QCD is reviewed. Using Abelian projection of the gauge potential which projects out the monopole potential gauge independently, we we show that there are two types of gluons: the color neutral binding gluons which plays the role of the confining agent and the colored valence gluons which become confined prisoners. With this we calculate the one-loop QCD effective potential and show the monopole condensation becomes the true vacuum of QCD. We propose to test the existence of two types of gluons experimentally by re-analyzing the existing gluon jets data.

Anomalies, renormalization group flows, and the a-theorem in six-dimensional (1, 0) theories

DOE PAGES

Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth

2016-10-17

We establish a linear relation between the a-type Weyl anomaly and the ’t Hooft anomaly coeffcients for the R-symmetry and gravitational anomalies in sixdimensional (1,0) superconformal field theories. For RG flows onto the tensor branch, where conformal symmetry is spontaneously broken, supersymmetry relates the anomaly mismatch Δa to the square of a four-derivative interaction for the dilaton. This establishes the a-theorem for all such flows. The four-derivative dilaton interaction is in turn related to the Green-Schwarz-like terms that are needed to match the ’t Hooft anomalies on the tensor branch, thus fixing their relation to Δa. We use our formulamore » to obtain exact expressions for the a-anomaly of N small E 8 instantons, as well as N M 5-branes probing an orbifold singularity, and verify the a-theorem for RG flows onto their Higgs branches. We also discuss aspects of supersymmetric RG flows that terminate in scale but not conformally invariant theories with massless gauge fields.« less

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

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

Ori, Amos

2010-11-15

Callan, Giddings, Harvey, and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

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.

A Non Local Electron Heat Transport Model for Multi-Dimensional Fluid Codes

NASA Astrophysics Data System (ADS)

Schurtz, Guy

2000-10-01

Apparent inhibition of thermal heat flow is one of the most ancient problems in computational Inertial Fusion and flux-limited Spitzer-Harm conduction has been a mainstay in multi-dimensional hydrodynamic codes for more than 25 years. Theoretical investigation of the problem indicates that heat transport in laser produced plasmas has to be considered as a non local process. Various authors contributed to the non local theory and proposed convolution formulas designed for practical implementation in one-dimensional fluid codes. Though the theory, confirmed by kinetic calculations, actually predicts a reduced heat flux, it fails to explain the very small limiters required in two-dimensional simulations. Fokker-Planck simulations by Epperlein, Rickard and Bell [PRL 61, 2453 (1988)] demonstrated that non local effects could lead to a strong reduction of heat flow in two dimensions, even in situations where a one-dimensional analysis suggests that the heat flow is nearly classical. We developed at CEA/DAM a non local electron heat transport model suitable for implementation in our two-dimensional radiation hydrodynamic code FCI2. This model may be envisionned as the first step of an iterative solution of the Fokker-Planck equations; it takes the mathematical form of multigroup diffusion equations, the solution of which yields both the heat flux and the departure of the electron distribution function to the Maxwellian. Although direct implementation of the model is straightforward, formal solutions of it can be expressed in convolution form, exhibiting a three-dimensional tensor propagator. Reduction to one dimension retrieves the original formula of Luciani, Mora and Virmont [PRL 51, 1664 (1983)]. Intense magnetic fields may be generated by thermal effects in laser targets; these fields, as well as non local effects, will inhibit electron conduction. We present simulations where both effects are taken into account and shortly discuss the coupling strategy between them.

F-theory and AdS3/CFT2 (2, 0)

NASA Astrophysics Data System (ADS)

Couzens, Christopher; Martelli, Dario; Schäfer-Nameki, Sakura

2018-06-01

We continue to develop the program initiated in [1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d N=(0,2) supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold Y_8^{τ } , which is elliptically fibered over a base \\tilde{M}_6 . We construct two classes of solutions given in terms of a product ansatz \\tilde{M}_6}=Σ × {M}_4 , where Σ is a complex curve and \\tilde{M}_4 is locally a Kähler surface. In the first class \\tilde{M}_4 is globally a Kähler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS3 × K3 × ℳ 5 τ , dual to 2d (0, 2) SCFTs, and AdS3 × S 3/Γ × CY 3, dual to 2d (0, 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d N=(2,2) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N=1 SCFTs.

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.

Higher winding strings and confined monopoles in N=2 supersymmetric QCD

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

Auzzi, R.; Bolognesi, S.; Shifman, M.

2010-04-15

We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet-Iliopoulos term {xi}{ne}0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany-Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in the N=(2,2) HT model. For spatially coinciding 2-strings, we findmore » three distinct minima of potential energy, corresponding to three different 2-strings. Then we find BPS-saturated kinks interpolating between each pair of vacua. Two kinks can be called elementary. They emanate one unit of the magnetic flux and have the same mass as the conventional 't Hooft-Polyakov monopole on the Coulomb branch of the bulk theory ({xi}=0). The third kink represents a composite bimonopole, with twice the minimal magnetic flux. Its mass is twice the mass of the elementary confined monopole. We find instantons in the HT model, and discuss quantum effects in composite strings at strong coupling. In addition, we study the renormalization group flow in this model.« less

t-topology on the n-dimensional Minkowski space

NASA Astrophysics Data System (ADS)

Agrawal, Gunjan; Shrivastava, Sampada

2009-05-01

In this paper, a topological study of the n-dimensional Minkowski space, n >1, with t-topology, denoted by Mt, has been carried out. This topology, unlike the usual Euclidean one, is more physically appealing being defined by means of the Lorentzian metric. It shares many topological properties with similar candidate topologies and it has the advantage of being first countable. Compact sets of Mt and continuous maps into Mt are studied using the notion of Zeno sequences besides characterizing those sets that have the same subspace topologies induced from the Euclidean and t-topologies on n-dimensional Minkowski space. A necessary and sufficient condition for a compact set in the Euclidean n-space to be compact in Mt is obtained, thereby proving that the n-cube, n >1, as a subspace of Mt, is not compact, while a segment on a timelike line is compact in Mt. This study leads to the nonsimply connectedness of Mt, for n =2. Further, Minkowski space with s-topology has also been dealt with.

Unparticle may be a remedy to the information loss in the scattering of fermion off dilaton black-hole

NASA Astrophysics Data System (ADS)

Rahaman, Anisur

2018-07-01

We study s-wave scattering of fermion off dilaton black-hole. With one loop correction it was found to suffer from nonpreservation of information and that of course, went against Hawking's revised suggestion on this issue. A nonstandard approach, e.g. the probable existence of unparticle in (1 + 1) dimension has been adopted here that shows a remedy to get rid of the danger of information loss to bring it in agrees with the Hawking's revised suggestion.

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.

On integrable boundaries in the 2 dimensional O(N) σ-models

NASA Astrophysics Data System (ADS)

Aniceto, Inês; Bajnok, Zoltán; Gombor, Tamás; Kim, Minkyoo; Palla, László

2017-09-01

We make an attempt to map the integrable boundary conditions for 2 dimensional non-linear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve.

Two-dimensional N = 2 Super-Yang-Mills Theory

NASA Astrophysics Data System (ADS)

August, Daniel; Wellegehausen, Björn; Wipf, Andreas

2018-03-01

Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.

Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime: exact spectrum

NASA Astrophysics Data System (ADS)

Destounis, Kyriakos; Panotopoulos, Grigoris; Rincón, Ángel

2018-02-01

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordström black hole is observed.

Gravitational waves from SU( N) glueball dark matter

DOE PAGES

Soni, Amarjit; Zhang, Yue

2017-05-30

Here, a hidden sector with pure non-abelian gauge symmetry is an elegant and just about the simplest model of dark matter. In this model the dark matter candidate is the lightest bound state made of the confined gauge fields, the dark glueball. In spite of its simplicity, the model has been shown to have several interesting non-standard implications in cosmology. In this work, we explore the gravitational waves from binary boson stars made of self-gravitating dark glueball fields as a natural and important consequence. We derive the dark SU(N) star mass and radius as functions of the only two fundamentalmore » parameters in the model, the glueball mass m and the number of colors N, and identify the regions that could be probed by the LIGO and future gravitational wave observatories.« less

Signatures of Higgs dilaton and critical Higgs inflation

NASA Astrophysics Data System (ADS)

García-Bellido, Juan

2018-01-01

We test the Higgs dilaton inflation model (HDM) using the latest cosmological datasets, including the cosmic microwave background temperature, polarization and lensing data from the Planck satellite (2015), the BICEP and Keck Array experiments, the type Ia supernovae from the JLA catalogue, the baryon acoustic oscillations from CMASS, LOWZ and 6dF, the weak lensing data from the CFHTLenS survey and the matter power spectrum measurements from the latest SDSS data release. We find that the values of all cosmological parameters allowed by the HDM are well within the Planck satellite (2015) constraints. In particular, we determine , , , and (at 95.5% c.l.). We also place new stringent constraints on the couplings of the HDM, ξχ<0.00328 and (at 95.5% c.l.). We find that the HDM is only slightly better than the w0waCDM model, with . Given that the HDM has two fewer parameters, we find Bayesian evidence favouring the HDM over the w0waCDM model. We also study the critical Higgs inflation model, taking into account the running of both the self-coupling λ(μ) and the non-minimal coupling to gravity ξ(μ). We find peaks in the curvature power spectrum at scales corresponding to the critical value μ that re-enter during the radiation era and collapse to form a broad distribution of clustered primordial black holes, which could constitute today the main

Two-dimensional electron gas in monolayer InN quantum wells

DOE PAGES

Pan, Wei; Dimakis, Emmanouil; Wang, George T.; ...

2014-11-24

We report in this letter experimental results that confirm the two-dimensional nature of the electron systems in monolayer InN quantum wells embedded in GaN barriers. The electron density and mobility of the two-dimensional electron system (2DES) in these InN quantum wells are 5×10 15 cm -2 and 420 cm 2 /Vs, respectively. Moreover, the diagonal resistance of the 2DES shows virtually no temperature dependence in a wide temperature range, indicating the topological nature of the 2DES.

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.

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings

NASA Astrophysics Data System (ADS)

Ganor, Ori J.

2018-02-01

"Curvepole (2,0)-theory" is a deformation of the (2,0)-theory with nonlocal interactions. A curvepole is defined as a two-dimensional generalization of a dipole. It is an object of fixed two-dimensional shape of which the boundary is a charged curve that interacts with a 2-form gauge field. Curvepole theory was previously only defined indirectly via M-theory. Here, we propose a supersymmetric Lagrangian, constructed explicitly up to quartic terms, for an "Abelian" curvepole theory, which is an interacting deformation of the free (2,0) tensor multiplet. This theory contains fields of which the quanta are curvepoles (i.e., fixed-shape strings). Supersymmetry is preserved (at least up to quartic terms) if the shape of the curvepoles is (two-dimensional) planar. This nonlocal six-dimensional quantum field theory may also serve as a UV completion for certain (local) five-dimensional gauge theories.

Non-Abelian vortices of higher winding numbers

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

Eto, Minoru; Konishi, Kenichi; Vinci, Walter

2006-09-15

We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of coaxial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto and Tong and by Auzzi, Shifman, and Yung. We find that it is a weighted projective space WCP{sub (2,1,1)}{sup 2}{approx_equal}CP{sup 2}/Z{sub 2}. This manifold contains an A{sub 1}-type (Z{sub 2}) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are thenmore » generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.« less

The resistance of an n-dimensional tetrahedron

NASA Astrophysics Data System (ADS)

Griffiths, Martin

2013-01-01

We consider here a problem that is suitable for introducing high-school students to the notion of generalizing shapes and solids to n dimensions. In particular, we calculate the effective resistance between any two vertices of an n-dimensional tetrahedron whose edges are each 1-Ω resistors. This leads, in a natural way, to more demanding problems, and indeed ideas for more advanced work in this area are also suggested.

N-Dimensional LLL Reduction Algorithm with Pivoted Reflection

PubMed Central

Deng, Zhongliang; Zhu, Di

2018-01-01

The Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm and many of its variants have been widely used by cryptography, multiple-input-multiple-output (MIMO) communication systems and carrier phase positioning in global navigation satellite system (GNSS) to solve the integer least squares (ILS) problem. In this paper, we propose an n-dimensional LLL reduction algorithm (n-LLL), expanding the Lovász condition in LLL algorithm to n-dimensional space in order to obtain a further reduced basis. We also introduce pivoted Householder reflection into the algorithm to optimize the reduction time. For an m-order positive definite matrix, analysis shows that the n-LLL reduction algorithm will converge within finite steps and always produce better results than the original LLL reduction algorithm with n > 2. The simulations clearly prove that n-LLL is better than the original LLL in reducing the condition number of an ill-conditioned input matrix with 39% improvement on average for typical cases, which can significantly reduce the searching space for solving ILS problem. The simulation results also show that the pivoted reflection has significantly declined the number of swaps in the algorithm by 57%, making n-LLL a more practical reduction algorithm. PMID:29351224

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)

Mass gap in the weak coupling limit of (2 +1 )-dimensional SU(2) lattice gauge theory

NASA Astrophysics Data System (ADS)

Anishetty, Ramesh; Sreeraj, T. P.

2018-04-01

We develop the dual description of (2 +1 )-dimensional SU(2) lattice gauge theory as interacting "Abelian-like" electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge invariant theory which in turn makes dynamics more transparent. Using path integral representation in phase space, the interacting closed loop dynamics is analyzed in the weak coupling limit to get the mass gap.

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.

Low-dimensional approximation searching strategy for transfer entropy from non-uniform embedding

PubMed Central

2018-01-01

Transfer entropy from non-uniform embedding is a popular tool for the inference of causal relationships among dynamical subsystems. In this study we present an approach that makes use of low-dimensional conditional mutual information quantities to decompose the original high-dimensional conditional mutual information in the searching procedure of non-uniform embedding for significant variables at different lags. We perform a series of simulation experiments to assess the sensitivity and specificity of our proposed method to demonstrate its advantage compared to previous algorithms. The results provide concrete evidence that low-dimensional approximations can help to improve the statistical accuracy of transfer entropy in multivariate causality analysis and yield a better performance over other methods. The proposed method is especially efficient as the data length grows. PMID:29547669

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.

Non-classical photon correlation in a two-dimensional photonic lattice.

PubMed

Gao, Jun; Qiao, Lu-Feng; Lin, Xiao-Feng; Jiao, Zhi-Qiang; Feng, Zhen; Zhou, Zheng; Gao, Zhen-Wei; Xu, Xiao-Yun; Chen, Yuan; Tang, Hao; Jin, Xian-Min

2016-06-13

Quantum interference and quantum correlation, as two main features of quantum optics, play an essential role in quantum information applications, such as multi-particle quantum walk and boson sampling. While many experimental demonstrations have been done in one-dimensional waveguide arrays, it remains unexplored in higher dimensions due to tight requirement of manipulating and detecting photons in large-scale. Here, we experimentally observe non-classical correlation of two identical photons in a fully coupled two-dimensional structure, i.e. photonic lattice manufactured by three-dimensional femtosecond laser writing. Photon interference consists of 36 Hong-Ou-Mandel interference and 9 bunching. The overlap between measured and simulated distribution is up to 0.890 ± 0.001. Clear photon correlation is observed in the two-dimensional photonic lattice. Combining with controllably engineered disorder, our results open new perspectives towards large-scale implementation of quantum simulation on integrated photonic chips.

DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term

NASA Astrophysics Data System (ADS)

Kovensky, Nicolas; Michalski, Gustavo; Schvellinger, Martin

2018-04-01

We calculate the structure function F 3( x, q 2) of the hadronic tensor of deep inelastic scattering (DIS) of charged leptons from glueballs of N=4 SYM theory at strong coupling and at small values of the Bjorken parameter in the gauge/string theory duality framework. This is done in terms of type IIB superstring theory scattering amplitudes. From the AdS5 perspective, the relevant part of the scattering amplitude comes from the five-dimensional non-Abelian Chern-Simons terms in the SU(4) gauged supergravity obtained from dimensional reduction on S 5. From type IIB superstring theory we derive an effective Lagrangian describing the four-point interaction in the local approximation. The exponentially small regime of the Bjorken parameter is investigated using Pomeron techniques.

Thermodynamic properties of charged three-dimensional black holes in the scalar-tensor gravity theory

NASA Astrophysics Data System (ADS)

Dehghani, M.

2018-02-01

Making use of the suitable transformation relations, the action of three-dimensional Einstein-Maxwell-dilaton gravity theory has been obtained from that of scalar-tensor modified gravity theory coupled to the Maxwell's electrodynamics as the matter field. Two new classes of the static three-dimensional charged dilatonic black holes, as the exact solutions to the coupled scalar, electromagnetic and gravitational field equations, have been obtained in the Einstein frame. Also, it has been found that the scalar potential can be written in the form of a generalized Liouville-type potential. The conserved black hole charge and masses as well as the black entropy, temperature, and electric potential have been calculated from the geometrical and thermodynamical approaches, separately. Through comparison of the results arisen from these two alternative approaches, the validity of the thermodynamical first law has been proved for both of the new black hole solutions in the Einstein frame. Making use of the canonical ensemble method, a black hole stability or phase transition analysis has been performed. Regarding the black hole heat capacity, with the black hole charge as a constant, the points of type-1 and type-2 phase transitions have been determined. Also, the ranges of the black hole horizon radius at which the Einstein black holes are thermally stable have been obtained for both of the new black hole solutions. Then making use of the inverse transformation relations, two new classes of the string black hole solutions have been obtained from their Einstein counterpart. The thermodynamics and thermal stability of the new string black hole solutions have been investigated. It has been found that thermodynamic properties of the new charged black holes are identical in the Einstein and Jordan frames.

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.

Low-resistance gateless high electron mobility transistors using three-dimensional inverted pyramidal AlGaN/GaN surfaces

NASA Astrophysics Data System (ADS)

So, Hongyun; Senesky, Debbie G.

2016-01-01

In this letter, three-dimensional gateless AlGaN/GaN high electron mobility transistors (HEMTs) were demonstrated with 54% reduction in electrical resistance and 73% increase in surface area compared with conventional gateless HEMTs on planar substrates. Inverted pyramidal AlGaN/GaN surfaces were microfabricated using potassium hydroxide etched silicon with exposed (111) surfaces and metal-organic chemical vapor deposition of coherent AlGaN/GaN thin films. In addition, electrical characterization of the devices showed that a combination of series and parallel connections of the highly conductive two-dimensional electron gas along the pyramidal geometry resulted in a significant reduction in electrical resistance at both room and high temperatures (up to 300 °C). This three-dimensional HEMT architecture can be leveraged to realize low-power and reliable power electronics, as well as harsh environment sensors with increased surface area.

Wet-chemical synthesis and applications of non-layer structured two-dimensional nanomaterials

PubMed Central

Tan, Chaoliang; Zhang, Hua

2015-01-01

Non-layer structured nanomaterials with single- or few-layer thickness have two-dimensional sheet-like structures and possess intriguing properties. Recent years have seen major advances in development of a host of non-layer structured ultrathin two-dimensional nanomaterials such as noble metals, metal oxides and metal chalcogenides. The wet-chemical synthesis has emerged as the most promising route towards high-yield and mass production of such nanomaterials. These nanomaterials are now finding increasing applications in a wide range of areas including catalysis, energy production and storage, sensor and nanotherapy, to name but a few. PMID:26303763

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.

Multinuclear nanoliter one-dimensional and two-dimensional NMR spectroscopy with a single non-resonant microcoil

NASA Astrophysics Data System (ADS)

Fratila, Raluca M.; Gomez, M. Victoria; Sýkora, Stanislav; Velders, Aldrik H.

2014-01-01

Nuclear magnetic resonance (NMR) spectroscopy is a powerful analytical technique, but its low sensitivity and highly sophisticated, costly, equipment severely constrain more widespread applications. Here we show that a non-resonant planar transceiver microcoil integrated in a microfluidic chip (detection volume 25 nl) can detect different nuclides in the full broad-band range of Larmor frequencies (at 9.4 T from 61 to 400 MHz). Routine one-dimensional (1D) and two-dimensional (2D), homo- and heteronuclear experiments can be carried out using the broad-band coil set-up. Noteworthy, heteronuclear 2D experiments can be performed in a straightforward manner on virtually any combination of nuclides (from classical 1H-13C to more exotic combinations like 19F-31P) both in coupled and decoupled mode. Importantly, the concept of a non-resonant system provides magnetic field-independent NMR probes; moreover, the small-volume alleviates problems related to field inhomogeneity, making the broad-band coil an attractive option for, for example, portable and table-top NMR systems.

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

An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton

DOE PAGES

Allison, Kyle; Hill, Christopher T.; Ross, Graham G.

2014-12-29

In the context of a Coleman–Weinberg mechanism for the Higgs boson mass, we address the strong CP problem. We show that a DFSZ-like invisible axion model with a gauge-singlet complex scalar field S, whose couplings to the Standard Model are naturally ultra-weak, can solve the strong CP problem and simultaneously generate acceptable electroweak symmetry breaking. The ultra-weak couplings of the singlet S are associated with underlying approximate shift symmetries that act as custodial symmetries and maintain technical naturalness. The model also contains a very light pseudo-Goldstone dilaton that is consistent with cosmological Polonyi bounds, and the axion can be themore » dark matter of the universe. As a result, we further outline how a SUSY version of this model, which may be required in the context of Grand Unification, can avoid introducing a hierarchy problem.« less

An ultra-weak sector, the strong CP problem and the pseudo-Goldstone dilaton

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

Allison, Kyle; Hill, Christopher T.; Ross, Graham G.

In the context of a Coleman–Weinberg mechanism for the Higgs boson mass, we address the strong CP problem. We show that a DFSZ-like invisible axion model with a gauge-singlet complex scalar field S, whose couplings to the Standard Model are naturally ultra-weak, can solve the strong CP problem and simultaneously generate acceptable electroweak symmetry breaking. The ultra-weak couplings of the singlet S are associated with underlying approximate shift symmetries that act as custodial symmetries and maintain technical naturalness. The model also contains a very light pseudo-Goldstone dilaton that is consistent with cosmological Polonyi bounds, and the axion can be themore » dark matter of the universe. As a result, we further outline how a SUSY version of this model, which may be required in the context of Grand Unification, can avoid introducing a hierarchy problem.« less

Effects of floating gate structures on the two-dimensional electron gas density and electron mobility in AlGaN/AlN/GaN heterostructure field-effect transistors

NASA Astrophysics Data System (ADS)

Zhao, Jingtao; Zhao, Zhenguo; Chen, Zidong; Lin, Zhaojun; Xu, Fukai

2017-12-01

In this study, we have investigated the electrical properties of the AlGaN/AlN/GaN heterostructure field-effect transistors (HFETs) with floating gate structures using the measured capacitancevoltage (C-V) and current-voltage (I-V) characteristics. It is found that the two-dimensional electron gas (2DEG) density under the central gate cannot be changed by the floating gate structures. However, the floating gate structures can cause the strain variation in the barrier layer, which lead to the non-uniform distribution of the polarization charges, then induce a polarization Coulomb field and scatter the 2DEG. More floating gate structures and closer distance between the floating gates and the central gate will result in stronger scattering effect of the 2DEG.

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.

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.

Interplay between the Dzyaloshinskii-Moriya term and external fields on spin transport in the spin-1/2 one-dimensional antiferromagnet

NASA Astrophysics Data System (ADS)

Lima, L. S.

2018-05-01

We study the effect of the uniform Dzyaloshinskii-Moriya interaction (symmetric exchange anisotropy) and arbitrary oriented external magnetic fields on spin conductivity in the spin-1/2 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated employing abelian bosonization and the Kubo formalism of transport. We investigate the influence of three competing phases at zero-temperature, (Néel phase, dimerized phase and gapless Luttinger liquid phase) on the AC spin conductivity.

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.

The hypermultiplet with Heisenberg isometry in N = 2 global and local supersymmetry

NASA Astrophysics Data System (ADS)

Ambrosetti, Nicola; Antoniadis, Ignatios; Derendinger, Jean-Pierre; Tziveloglou, Pantelis

2011-06-01

The string coupling of N = 2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hyper-multiplet, that has four real scalars living on a quaternion-Kähler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kähler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

NASA Technical Reports Server (NTRS)

Risch, Tim; Kostyk, Chris

2016-01-01

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be

Four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

NASA Astrophysics Data System (ADS)

Luo, Yuan; Tan, Meng-Chwan; Vasko, Petr; Zhao, Qin

2017-05-01

We perform a series of dimensional reductions of the 6d, \\mathcal{N} = (2, 0) SCFT on S 2 × Σ × I × S 1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S 1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S 2 × Σ × I, (ii) a further reduction on S 2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S 2 and S 1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an \\mathcal{N} = 2 supersymmetric theory on S 2 × I × S 1, our results imply a 4d-2d duality between four-dimensional \\mathcal{N} = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

T-duality invariant effective actions at orders α', α'2

NASA Astrophysics Data System (ADS)

Razaghian, Hamid; Garousi, Mohammad R.

2018-02-01

We use compatibility of the D-dimensional effective actions for diagonal metric and for dilaton with the T-duality when theory is compactified on a circle, to find the D-dimensional couplings of curvatures and dilaton as well as the higher derivative corrections to the ( D - 1)-dimensional Buscher rules at orders α' and α'2. We observe that the T-duality constraint on the effective actions fixes the covariant effective actions at each order of α' up to field redefinitions and up to an overall factor. Inspired by these results, we speculate that the D-dimensional effective actions at any order of α' must be consistent with the standard Buscher rules provided that one uses covariant field redefinitions in the corresponding reduced ( D - 1)-dimensional effective actions. This constraint may be used to find effective actions at all higher orders of α'.

Spontaneous supersymmetry breaking in two dimensional lattice super QCD

DOE PAGES

Catterall, Simon; Veernala, Aarti

2015-10-02

We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U(N c) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetrymore » breaks spontaneously when N f < N c in agreement with theoretical expectations.« less

Holographic QCD phase diagram with critical point from Einstein-Maxwell-dilaton dynamics

NASA Astrophysics Data System (ADS)

Knaute, J.; Yaresko, R.; Kämpfer, B.

2018-03-01

Supplementing the holographic Einstein-Maxwell-dilaton model of [1,2] by input of lattice QCD data for 2 + 1 flavors and physical quark masses for the equation of state and quark number susceptibility at zero baryo-chemical potential we explore the resulting phase diagram over the temperature-chemical potential plane. A first-order phase transition sets in at a temperature of about 112 MeV and a baryo-chemical potential of 612 MeV. We estimate the accuracy of the critical point position in the order of approximately 5-8% by considering parameter variations and different low-temperature asymptotics for the second-order quark number susceptibility. The critical pressure as a function of the temperature has a positive slope, i.e. the entropy per baryon jumps up when crossing the phase border line from larger values of temperature/baryo-chemical potential, thus classifying the phase transition as a gas-liquid one. The updated holographic model exhibits in- and outgoing isentropes in the vicinity of the first-order phase transition.

Three-dimensional representations of photo-induced electron transfer rates in pyrene-(CH2)n-N,N'-dimethylaniline systems obtained by three electron transfer theories.

PubMed

Rujkorakarn, Rong; Tanaka, Fumio

2009-01-01

The observed rates of photo-induced electron transfer (ET) from N,N'-dimethylaniline (DMA) to the excited pyrene (Py) in confined systems of pyrene-(CH(2))(n)-N,N'- dimethylaniline (PnD: n=1-3) were studied by molecular dynamic simulation (MD) and three kinds of electron transfer theories. ET parameters contained in Marcus theory (M theory), Bixon and Jortner theory (BJ theory) and Kakitani and Mataga theory (KM theory) were determined so as to fit the calculated fluorescence intensities with those obtained by the observed ET rates, according to a non-linear least squares method. Three-dimensional profiles of logarithm of calculated ET rates depending on two of three ET parameters, R, epsilon(0) and -DeltaG degrees were systematically examined with best-fit ET parameters of P1D. Bell shape dependencies of ET rate were predicted on R and on epsilon(0), and on -DeltaG degrees as well, by M theory and KM theory. The profiles of logarithm of ET rate calculated by BJ theory exhibited oscillatory dependencies not only on -DeltaG degrees , but also on R and on epsilon(0). Relationship between ET state and charge transfer complex was discussed with BJ theory.

General n-dimensional quadrature transform and its application to interferogram demodulation.

PubMed

Servin, Manuel; Quiroga, Juan Antonio; Marroquin, Jose Luis

2003-05-01

Quadrature operators are useful for obtaining the modulating phase phi in interferometry and temporal signals in electrical communications. In carrier-frequency interferometry and electrical communications, one uses the Hilbert transform to obtain the quadrature of the signal. In these cases the Hilbert transform gives the desired quadrature because the modulating phase is monotonically increasing. We propose an n-dimensional quadrature operator that transforms cos(phi) into -sin(phi) regardless of the frequency spectrum of the signal. With the quadrature of the phase-modulated signal, one can easily calculate the value of phi over all the domain of interest. Our quadrature operator is composed of two n-dimensional vector fields: One is related to the gradient of the image normalized with respect to local frequency magnitude, and the other is related to the sign of the local frequency of the signal. The inner product of these two vector fields gives us the desired quadrature signal. This quadrature operator is derived in the image space by use of differential vector calculus and in the frequency domain by use of a n-dimensional generalization of the Hilbert transform. A robust numerical algorithm is given to find the modulating phase of two-dimensional single-image closed-fringe interferograms by use of the ideas put forward.

Electronic and Optical Properties of Two-Dimensional GaN from First-Principles.

PubMed

Sanders, Nocona; Bayerl, Dylan; Shi, Guangsha; Mengle, Kelsey A; Kioupakis, Emmanouil

2017-12-13

Gallium nitride (GaN) is an important commercial semiconductor for solid-state lighting applications. Atomically thin GaN, a recently synthesized two-dimensional material, is of particular interest because the extreme quantum confinement enables additional control of its light-emitting properties. We performed first-principles calculations based on density functional and many-body perturbation theory to investigate the electronic, optical, and excitonic properties of monolayer and bilayer two-dimensional (2D) GaN as a function of strain. Our results demonstrate that light emission from monolayer 2D GaN is blueshifted into the deep ultraviolet range, which is promising for sterilization and water-purification applications. Light emission from bilayer 2D GaN occurs at a similar wavelength to its bulk counterpart due to the cancellation of the effect of quantum confinement on the optical gap by the quantum-confined Stark shift. Polarized light emission at room temperature is possible via uniaxial in-plane strain, which is desirable for energy-efficient display applications. We compare the electronic and optical properties of freestanding two-dimensional GaN to atomically thin GaN wells embedded within AlN barriers in order to understand how the functional properties are influenced by the presence of barriers. Our results provide microscopic understanding of the electronic and optical characteristics of GaN at the few-layer regime.

Use of 15N reverse gradient two-dimensional nuclear magnetic resonance spectroscopy to follow metabolic activity in Nicotiana plumbaginifolia cell-suspension cultures.

PubMed

Mesnard, F; Azaroual, N; Marty, D; Fliniaux, M A; Robins, R J; Vermeersch, G; Monti, J P

2000-02-01

Nitrogen metabolism was monitored in suspension cultured cells of Nicotiana plumbaginifolia Viv. using nuclear magnetic resonance (NMR) spectroscopy following the feeding of (15NH4)2SO4 and K15NO3. By using two-dimensional 15N-1H NMR with heteronuclear single-quantum-coherence spectroscopy and heteronuclear multiple-bond-coherence spectroscopy sequences, an enhanced resolution of the incorporation of 15N label into a range of compounds could be detected. Thus, in addition to the amino acids normally observed in one-dimensional 15N NMR (glutamine, aspartate, alanine), several other amino acids could be resolved, notably serine, glycine and proline. Furthermore, it was found that the peak normally assigned to the non-protein amino-acid gamma-aminobutyric acid in the one-dimensional 15N NMR spectrum was resolved into a several components. A peak of N-acetylated compounds was resolved, probably composed of the intermediates in arginine biosynthesis, N-acetylglutamate and N-acetylornithine and, possibly, the intermediate of putrescine degradation into gamma-aminobutyric acid, N-acetylputrescine. The occurrence of 15N-label in agmatine and the low detection of labelled putrescine indicate that crucial intermediates of the pathway from glutamate to polyamines and/or the tobacco alkaloids could be monitored. For the first time, labelling of the peptide glutathione and of the nucleotide uridine could be seen.

CMB power spectrum contribution from cosmic strings using field-evolution simulations of the Abelian Higgs model

NASA Astrophysics Data System (ADS)

Bevis, Neil; Hindmarsh, Mark; Kunz, Martin; Urrestilla, Jon

2007-03-01

We present the first field-theoretic calculations of the contribution made by cosmic strings to the temperature power spectrum of the cosmic microwave background (CMB). Unlike previous work, in which strings were modeled as idealized one-dimensional objects, we evolve the simplest example of an underlying field theory containing local U(1) strings, the Abelian Higgs model. Limitations imposed by finite computational volumes are overcome using the scaling property of string networks and a further extrapolation related to the lessening of the string width in comoving coordinates. The strings and their decay products, which are automatically included in the field theory approach, source metric perturbations via their energy-momentum tensor, the unequal-time correlation functions of which are used as input into the CMB calculation phase. These calculations involve the use of a modified version of CMBEASY, with results provided over the full range of relevant scales. We find that the string tension μ required to normalize to the WMAP 3-year data at multipole ℓ=10 is Gμ=[2.04±0.06(stat.)±0.12(sys.)]×10-6, where we have quoted statistical and systematic errors separately, and G is Newton’s constant. This is a factor 2 3 higher than values in current circulation.

Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

NASA Astrophysics Data System (ADS)

Makino, Hiroki; Suzuki, Hiroshi

2015-03-01

It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D O(N) non-linear sigma model possesses a similar property: The flowed N-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a (2+1)-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the O(N) non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.

Three dimensional, non-linear, finite element analysis of compactable soil interaction with a hyperelastic wheel

NASA Astrophysics Data System (ADS)

Chiroux, Robert Charles

The objective of this research was to produce a three dimensional, non-linear, dynamic simulation of the interaction between a hyperelastic wheel rolling over compactable soil. The finite element models developed to produce the simulation utilized the ABAQUS/Explicit computer code. Within the simulation two separate bodies were modeled, the hyperelastic wheel and a compactable soil-bed. Interaction between the bodies was achieved by allowing them to come in contact but not to penetrate the contact surface. The simulation included dynamic loading of a hyperelastic, rubber tire in contact with compactable soil with an applied constant angular velocity or torque, including a tow load, applied to the wheel hub. The constraints on the wheel model produced a straight and curved path. In addition the simulation included a shear limit between the tire and soil allowing for the introduction of slip. Soil properties were simulated using the Drucker-Prager, Cap Plasticity model available within the ABAQUS/Explicit program. Numerical results obtained from the three dimensional model were compared with related experimental data and showed good correlation for similar conditions. Numerical and experimental data compared well for both stress and wheel rut formation depth under a weight of 5.8 kN and a constant angular velocity applied to the wheel hub. The simulation results provided a demonstration of the benefit of three-dimensional simulation in comparison to previous two-dimensional, plane strain simulations.

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

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.

On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Nolan, Brien C.; Winstanley, Elizabeth

2016-02-01

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

Effect of the refractive index on the hawking temperature: an application of the Hamilton-Jacobi method

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

Sakalli, I., E-mail: izzet.sakalli@emu.edu.tr; Mirekhtiary, S. F., E-mail: fatemeh.mirekhtiary@emu.edu.tr

2013-10-15

Hawking radiation of a non-asymptotically flat 4-dimensional spherically symmetric and static dilatonic black hole (BH) via the Hamilton-Jacobi (HJ) method is studied. In addition to the naive coordinates, we use four more different coordinate systems that are well-behaved at the horizon. Except for the isotropic coordinates, direct computation by the HJ method leads to the standard Hawking temperature for all coordinate systems. The isotropic coordinates allow extracting the index of refraction from the Fermat metric. It is explicitly shown that the index of refraction determines the value of the tunneling rate and its natural consequence, the Hawking temperature. The isotropicmore » coordinates in the conventional HJ method produce a wrong result for the temperature of the linear dilaton. Here, we explain how this discrepancy can be resolved by regularizing the integral possessing a pole at the horizon.« less

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.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

2016-10-01

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 = (2, 2) supersymmetry to the chiral one, 𝒩 = (0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Beta Functions in Chirally Deformed Supersymmetric Sigma Models in Two Dimensions

NASA Astrophysics Data System (ADS)

Vainshtein, Arkady

We study two-dimensional sigma models where the chiral deformation diminished the original 𝒩 =(2, 2) supersymmetry to the chiral one, 𝒩 =(0, 2). Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional 𝒩 = 1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Preoperative (3-dimensional) computed tomography lung reconstruction before anatomic segmentectomy or lobectomy for stage I non-small cell lung cancer.

PubMed

Chan, Ernest G; Landreneau, James R; Schuchert, Matthew J; Odell, David D; Gu, Suicheng; Pu, Jiantao; Luketich, James D; Landreneau, Rodney J

2015-09-01

Accurate cancer localization and negative resection margins are necessary for successful segmentectomy. In this study, we evaluate a newly developed software package that permits automated segmentation of the pulmonary parenchyma, allowing 3-dimensional assessment of tumor size, location, and estimates of surgical margins. A pilot study using a newly developed 3-dimensional computed tomography analytic software package was performed to retrospectively evaluate preoperative computed tomography images of patients who underwent segmentectomy (n = 36) or lobectomy (n = 15) for stage 1 non-small cell lung cancer. The software accomplishes an automated reconstruction of anatomic pulmonary segments of the lung based on bronchial arborization. Estimates of anticipated surgical margins and pulmonary segmental volume were made on the basis of 3-dimensional reconstruction. Autosegmentation was achieved in 72.7% (32/44) of preoperative computed tomography images with slice thicknesses of 3 mm or less. Reasons for segmentation failure included local severe emphysema or pneumonitis, and lower computed tomography resolution. Tumor segmental localization was achieved in all autosegmented studies. The 3-dimensional computed tomography analysis provided a positive predictive value of 87% in predicting a marginal clearance greater than 1 cm and a 75% positive predictive value in predicting a margin to tumor diameter ratio greater than 1 in relation to the surgical pathology assessment. This preoperative 3-dimensional computed tomography analysis of segmental anatomy can confirm the tumor location within an anatomic segment and aid in predicting surgical margins. This 3-dimensional computed tomography information may assist in the preoperative assessment regarding the suitability of segmentectomy for peripheral lung cancers. Published by Elsevier Inc.

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.

DC conductivity with external magnetic field in hyperscaling violating geometry

NASA Astrophysics Data System (ADS)

Bhatnagar, Neha; Siwach, Sanjay

2018-02-01

We investigate the holographic DC conductivity of (2+1)-dimensional systems while considering hyperscaling violating geometry in bulk. We consider Einstein-Maxwell-dilaton system with two gauge fields and Liouville-type potential for dilaton. We also consider axionic fields in bulk to introduce momentum relaxation in the system. We apply an external magnetic field to study the response of the system and obtain analytic expressions for DC conductivity, Hall angle and (thermo)electric conductivity.

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

NASA Astrophysics Data System (ADS)

Deta, U. A.; Lestari, N. A.; Yantidewi, M.; Suparmi, A.; Cari, C.

2018-03-01

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

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

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested firstmore » by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.« less

D-type conformal matter and SU/USp quivers

NASA Astrophysics Data System (ADS)

Kim, Hee-Cheol; Razamat, Shlomo S.; Vafa, Cumrun; Zafrir, Gabi

2018-06-01

We discuss the four dimensional models obtained by compactifying a single M5 brane probing D N singularity (minimal D-type (1 , 0) conformal matter in six dimensions) on a torus with flux for abelian subgroups of the SO(4 N) flavor symmetry. We derive the resulting quiver field theories in four dimensions by first compactifying on a circle and relating the flux to duality domain walls in five dimensions. This leads to novel N=1 dualities in 4 dimensions which arise from distinct five dimensional realizations of the circle compactifications of the D-type conformal matter.

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

NASA Astrophysics Data System (ADS)

Ghosh, Surya K.; Cherstvy, Andrey G.; Grebenkov, Denis S.; Metzler, Ralf

2016-01-01

A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

A Three-Dimensional Pore-Scale Model for Non-Wetting Phase Mobilization with Ferrofluid

NASA Astrophysics Data System (ADS)

Wang, N.; Prodanovic, M.

2017-12-01

Ferrofluid, a stable dispersion of paramagnetic nanoparticles in water, can generate a distributed pressure difference across the phase interface in an immiscible two-phase flow under an external magnetic field. In water-wet porous media, this non-uniform pressure difference may be used to mobilize the non-wetting phase, e.g. oil, trapped in the pores. Previous numerical work by Soares et al. of two-dimensional single-pore model showed enhanced non-wetting phase recovery with water-based ferrofluid under certain magnetic field directions and decreased recovery under other directions. However, the magnetic field selectively concentrates in the high magnetic permeability ferrofluid which fills the small corners between the non-wetting phase and the solid wall. The magnetic field induced pressure is proportional to the square of local magnetic field strength and its normal component, and makes a significant impact on the non-wetting phase deformation. The two-dimensional model omitted the effect of most of these corners and is not sufficient to compute the magnetic-field-induced pressure difference or to predict the non-wetting blob deformation. Further, it is not clear that 3D effects on magnetic field in an irregular geometry can be approximated in 2D. We present a three-dimensional immiscible two-phase flow model to simulate the deformation of a non-wetting liquid blob in a single pore filled with a ferrofluid under a uniform external magnetic field. The ferrofluid is modeled as a uniform single phase because the nanoparticles are 104 times smaller than the pore. The open source CFD solver library OpenFOAM is used for the simulations based on the volume of fluid method. Simulations are performed in a converging-diverging channel model on different magnetic field direction, different initial oil saturations, and different pore shapes. Results indicate that the external magnetic field always stretches the non-wetting blob away from the solid channel wall. A magnetic

Non-localized trapping effects in AlGaN/GaN heterojunction field-effect transistors subjected to on-state bias stress

NASA Astrophysics Data System (ADS)

Hu, Cheng-Yu; Hashizume, Tamotsu

2012-04-01

For AlGaN/GaN heterojunction field-effect transistors, on-state-bias-stress (on-stress)-induced trapping effects were observed across the entire drain access region, not only at the gate edge. However, during the application of on-stress, the highest electric field was only localized at the drain side of the gate edge. Using the location of the highest electric field as a reference, the trapping effects at the gate edge and at the more distant access region were referred to as localized and non-localized trapping effect, respectively. Using two-dimensional-electron-gas sensing-bar (2DEG-sensing-bar) and dual-gate structures, the non-localized trapping effects were investigated and the trap density was measured to be ˜1.3 × 1012 cm-2. The effect of passivation was also discussed. It was found that both surface leakage currents and hot electrons are responsible for the non-localized trapping effects with hot electrons having the dominant effect. Since hot electrons are generated from the 2DEG channel, it is highly likely that the involved traps are mainly in the GaN buffer layer. Using monochromatic irradiation (1.24-2.81 eV), the trap levels responsible for the non-localized trapping effects were found to be located at 0.6-1.6 eV from the valence band of GaN. Both trap-assisted impact ionization and direct channel electron injection are proposed as the possible mechanisms of the hot-electron-related non-localized trapping effect. Finally, using the 2DEG-sensing-bar structure, we directly confirmed that blocking gate injected electrons is an important mechanism of Al2O3 passivation.

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.

Non-equilibrium coherence dynamics in one-dimensional Bose gases.

PubMed

Hofferberth, S; Lesanovsky, I; Fischer, B; Schumm, T; Schmiedmayer, J

2007-09-20

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.

Kaluza-Klein theories as a tool to find new gauge symmetries

NASA Astrophysics Data System (ADS)

Dolan, L.

Non-abelian Kaluza-Klein theories are studied with respect to using the invariances of multi-dimensional general relativity to investigate hidden symmetry, such as Kac-Mody Lie algebras, of the four-dimensional Yang-Mills theory. Several properties of the affine transformations on the self-dual set are identified and are used to motivate the Kaluza-Klein analysis. In this context, a system of differential equations is derived for new symmetry transformations which may be extendable to the full gauge theory.

Exploring soft constraints on effective actions

NASA Astrophysics Data System (ADS)

Bianchi, Massimo; Guerrieri, Andrea L.; Huang, Yu-tin; Lee, Chao-Jung; Wen, Congkao

2016-10-01

We study effective actions for simultaneous breaking of space-time and internal symmetries. Novel features arise due to the mixing of Goldstone modes under the broken symmetries which, in contrast to the usual Adler's zero, leads to non-vanishing soft limits. Such scenarios are common for spontaneously broken SCFT's. We explicitly test these soft theorems for N=4 sYM in the Coulomb branch both perturbatively and non-perturbatively. We explore the soft constraints systematically utilizing recursion relations. In the pure dilaton sector of a general CFT, we show that all amplitudes up to order s n ˜ ∂2 n are completely determined in terms of the k-point amplitudes at order s k with k ≤ n. Terms with at most one derivative acting on each dilaton insertion are completely fixed and coincide with those appearing in the conformal DBI, i.e. DBI in AdS. With maximal supersymmetry, the effective actions are further constrained, leading to new non-renormalization theorems. In particular, the effective action is fixed up to eight derivatives in terms of just one unknown four-point coefficient and one more coefficient for ten-derivative terms. Finally, we also study the interplay between scale and conformal invariance in this context.

Observation of anomalous Hall effect in a non-magnetic two-dimensional electron system

PubMed Central

Maryenko, D.; Mishchenko, A. S.; Bahramy, M. S.; Ernst, A.; Falson, J.; Kozuka, Y.; Tsukazaki, A.; Nagaosa, N.; Kawasaki, M.

2017-01-01

Anomalous Hall effect, a manifestation of Hall effect occurring in systems without time-reversal symmetry, has been mostly observed in ferromagnetically ordered materials. However, its realization in high-mobility two-dimensional electron system remains elusive, as the incorporation of magnetic moments deteriorates the device performance compared to non-doped structure. Here we observe systematic emergence of anomalous Hall effect in various MgZnO/ZnO heterostructures that exhibit quantum Hall effect. At low temperatures, our nominally non-magnetic heterostructures display an anomalous Hall effect response similar to that of a clean ferromagnetic metal, while keeping a large anomalous Hall effect angle θAHE≈20°. Such a behaviour is consistent with Giovannini–Kondo model in which the anomalous Hall effect arises from the skew scattering of electrons by localized paramagnetic centres. Our study unveils a new aspect of many-body interactions in two-dimensional electron systems and shows how the anomalous Hall effect can emerge in a non-magnetic system. PMID:28300133

An improved three-dimensional non-scanning laser imaging system based on digital micromirror device

NASA Astrophysics Data System (ADS)

Xia, Wenze; Han, Shaokun; Lei, Jieyu; Zhai, Yu; Timofeev, Alexander N.

2018-01-01

Nowadays, there are two main methods to realize three-dimensional non-scanning laser imaging detection, which are detection method based on APD and detection method based on Streak Tube. However, the detection method based on APD possesses some disadvantages, such as small number of pixels, big pixel interval and complex supporting circuit. The detection method based on Streak Tube possesses some disadvantages, such as big volume, bad reliability and high cost. In order to resolve the above questions, this paper proposes an improved three-dimensional non-scanning laser imaging system based on Digital Micromirror Device. In this imaging system, accurate control of laser beams and compact design of imaging structure are realized by several quarter-wave plates and a polarizing beam splitter. The remapping fiber optics is used to sample the image plane of receiving optical lens, and transform the image into line light resource, which can realize the non-scanning imaging principle. The Digital Micromirror Device is used to convert laser pulses from temporal domain to spatial domain. The CCD with strong sensitivity is used to detect the final reflected laser pulses. In this paper, we also use an algorithm which is used to simulate this improved laser imaging system. In the last, the simulated imaging experiment demonstrates that this improved laser imaging system can realize three-dimensional non-scanning laser imaging detection.

Baryon and lepton number violating effective operators in a non-universal extension of the standard model

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

Fuentes-Martín, J.

2016-01-22

It is well known that non-abelian Yang-Mills theories present non-trivial minima of the action, the so-called instantons. In the context of electroweak theories these instanton solutions may induce violations of baryon and lepton number of the form ΔB = ΔL = n{sub f}, with n{sub f} being the number of families coupled to the gauge group. An interesting feature of these violations is that the flavor structure of the gauge couplings is inherited by the instanton transitions. This effect is generally neglected in the literature. We will show that the inclusion of flavor interactions in the instanton solutions may bemore » interesting in certain theoretical frameworks and will provide an approach to include these effects. In particular we will perform this implementation in the non-universal SU (2){sub l} ⊗SU (2){sub h} ⊗U (1){sub Y} model that singularizes the third family. Within this framework, we will use the instanton transitions to set a bound on the SU (2){sub h} gauge coupling.« less

Alfvén Turbulence Driven by High-Dimensional Interior Crisis in the Solar Wind

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Rempel, E. L.; Macau, E. E. N.; Rosa, R. R.; Christiansen, F.

2003-09-01

Alfvén intermittent turbulence has been observed in the solar wind. It has been previously shown that the interplanetary Alfvén intermittent turbulence can appear due to a low-dimensional temporal chaos [1]. In this paper, we study the nonlinear spatiotemporal dynamics of Alfvén waves governed by the Kuramoto-Sivashinsky equation which describes the phase evolution of a large-amplitude Alfvén wave. We investigate the Alfvén turbulence driven by a high-dimensional interior crisis, which is a global bifurcation caused by the collision of a chaotic attractor with an unstable periodic orbit. This nonlinear phenomenon is analyzed using the numerical solutions of the model equation. The identification of the unstable periodic orbits and their invariant manifolds is fundamental for understanding the instability, chaos and turbulence in complex systems such as the solar wind plasma. The high-dimensional dynamical system approach to space environment turbulence developed in this paper can improve our interpretation of the origin and the nature of Alfvén turbulence observed in the solar wind.

Supersonic N-Crowdions in a Two-Dimensional Morse Crystal

NASA Astrophysics Data System (ADS)

Dmitriev, S. V.; Korznikova, E. A.; Chetverikov, A. P.

2018-03-01

An interstitial atom placed in a close-packed atomic row of a crystal is called crowdion. Such defects are highly mobile; they can move along the row, transferring mass and energy. We generalize the concept of a classical supersonic crowdion to an N-crowdion in which not one but N atoms move simultaneously with a high velocity. Using molecular dynamics simulations for a close-packed two-dimensional Morse crystal, we show that N-crowdions transfer mass much more efficiently, because they are capable of covering large distances while having a lower total energy than that of a classical 1-crowdion.

Action-minimizing solutions of the one-dimensional N-body problem

NASA Astrophysics Data System (ADS)

Yu, Xiang; Zhang, Shiqing

2018-05-01

We supplement the following result of C. Marchal on the Newtonian N-body problem: A path minimizing the Lagrangian action functional between two given configurations is always a true (collision-free) solution when the dimension d of the physical space R^d satisfies d≥2. The focus of this paper is on the fixed-ends problem for the one-dimensional Newtonian N-body problem. We prove that a path minimizing the action functional in the set of paths joining two given configurations and having all the time the same order is always a true (collision-free) solution. Considering the one-dimensional N-body problem with equal masses, we prove that (i) collision instants are isolated for a path minimizing the action functional between two given configurations, (ii) if the particles at two endpoints have the same order, then the path minimizing the action functional is always a true (collision-free) solution and (iii) when the particles at two endpoints have different order, although there must be collisions for any path, we can prove that there are at most N! - 1 collisions for any action-minimizing path.

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.

Fast Multipole Methods for Three-Dimensional N-body Problems

NASA Technical Reports Server (NTRS)

Koumoutsakos, P.

1995-01-01

We are developing computational tools for the simulations of three-dimensional flows past bodies undergoing arbitrary motions. High resolution viscous vortex methods have been developed that allow for extended simulations of two-dimensional configurations such as vortex generators. Our objective is to extend this methodology to three dimensions and develop a robust computational scheme for the simulation of such flows. A fundamental issue in the use of vortex methods is the ability of employing efficiently large numbers of computational elements to resolve the large range of scales that exist in complex flows. The traditional cost of the method scales as Omicron (N(sup 2)) as the N computational elements/particles induce velocities at each other, making the method unacceptable for simulations involving more than a few tens of thousands of particles. In the last decade fast methods have been developed that have operation counts of Omicron (N log N) or Omicron (N) (referred to as BH and GR respectively) depending on the details of the algorithm. These methods are based on the observation that the effect of a cluster of particles at a certain distance may be approximated by a finite series expansion. In order to exploit this observation we need to decompose the element population spatially into clusters of particles and build a hierarchy of clusters (a tree data structure) - smaller neighboring clusters combine to form a cluster of the next size up in the hierarchy and so on. This hierarchy of clusters allows one to determine efficiently when the approximation is valid. This algorithm is an N-body solver that appears in many fields of engineering and science. Some examples of its diverse use are in astrophysics, molecular dynamics, micro-magnetics, boundary element simulations of electromagnetic problems, and computer animation. More recently these N-body solvers have been implemented and applied in simulations involving vortex methods. Koumoutsakos and Leonard (1995

Studying non-equilibrium many-body dynamics using one-dimensional Bose gases

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

Langen, Tim; Gring, Michael; Kuhnert, Maximilian

2014-12-04

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

THE GENERALIZATION OF SIERPINSKI CARPET AND MENGER SPONGE IN n-DIMENSIONAL SPACE

NASA Astrophysics Data System (ADS)

Yang, Yun; Feng, Yuting; Yu, Yanhua

In this paper, we generalize Sierpinski carpet and Menger sponge in n-dimensional space, by using the generations and characterizations of affinely-equivalent Sierpinski carpet and Menger sponge. Exactly, Menger sponge in 4-dimensional space could be drawn out clearly under an affine transformation. Furthermore, the method could be used to a much broader class in fractals.

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.

Fluxes, holography and twistors: String theory paths to four dimensions

NASA Astrophysics Data System (ADS)

Gao, Peng

2007-12-01

There are presently three popular paths to obtain four dimensional physics from string theory: compactification, holography and twistor space. We present results in this thesis on each of them, discussing the geometric structure of flux compactifications, the interplay between holography and S -duality in M-theory and the perturbative amplitudes of the marginally deformed super-Yang-Mills theory obtained from topological string theory on a supertwistor space. First we analyze supersymmetric flux compactifications of ten dimensional string theories to four dimensions. Back reaction of the fluxes on the six dimensional internal geometry is characterized by G-structures. In type IIB compactification on SU(3)-structure manifold with N = 1 supersymmetry, we solve the equations dictating the five components of intrinsic torsion. We find that the six dimensional manifold always retains an integrable almost complex structure compatible with supersymmetry. In terms of the various vacuum fields, the axion/dilaton is found to be generically non-holomorphic, and the four dimensional cosmological constant is nonvanishing only if the SU(3) structure group is reduced to SU(2). The equations are solved by one holomorphic function. Around the poles and zeros of the holomorphic function, the geometry locally looks like the well known type-A and type-B solutions. When this function is a constant, the geometry can be viewed as a holographic RG flow. After classifying the type IIB SU(3)-structure flux vacua, we analyze the effect of non-perturbative corrections on the moduli space of N = 2 flux compactifications. At energy below the Kaluza-Klein scale, the four dimensional effective theory is a gauged supergravity theory with vanishing cosmological constant. The gauging of isometries on the hyper-multiplet moduli space is induced by the fluxes. We show that instanton corrections which could potentially lift the gauged isometries are in fact prohibited both in the type IIA and heterotic

The non-commutative topology of two-dimensional dirty superconductors

NASA Astrophysics Data System (ADS)

De Nittis, Giuseppe; Schulz-Baldes, Hermann

2018-01-01

Non-commutative analysis tools have successfully been applied to the integer quantum Hall effect, in particular for a proof of the stability of the Hall conductance in an Anderson localization regime and of the bulk-boundary correspondence. In this work, these techniques are implemented to study two-dimensional dirty superconductors described by Bogoliubov-de Gennes Hamiltonians. After a thorough presentation of the basic framework and the topological invariants, Kubo formulas for the thermal, thermoelectric and spin Hall conductance are analyzed together with the corresponding edge currents.

A three-dimensional Dirichlet-to-Neumann operator for water waves over topography

NASA Astrophysics Data System (ADS)

Andrade, D.; Nachbin, A.

2018-06-01

Surface water waves are considered propagating over highly variable non-smooth topographies. For this three dimensional problem a Dirichlet-to-Neumann (DtN) operator is constructed reducing the numerical modeling and evolution to the two dimensional free surface. The corresponding Fourier-type operator is defined through a matrix decomposition. The topographic component of the decomposition requires special care and a Galerkin method is provided accordingly. One dimensional numerical simulations, along the free surface, validate the DtN formulation in the presence of a large amplitude, rapidly varying topography. An alternative, conformal mapping based, method is used for benchmarking. A two dimensional simulation in the presence of a Luneburg lens (a particular submerged mound) illustrates the accurate performance of the three dimensional DtN operator.

Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass

NASA Astrophysics Data System (ADS)

Zupan, E.; Zupan, D.

2018-01-01

In this paper, we present a coupled dynamic analysis of a moving particle on a deformable three-dimensional frame. The presented numerical model is capable of considering arbitrary curved and twisted initial geometry of the beam and takes into account geometric non-linearity of the structure. Coupled with dynamic equations of the structure, the equations of moving particle are solved. The moving particle represents the dynamic load and varies the mass distribution of the structure and at the same time its path is adapting due to deformability of the structure. A coupled geometrically non-linear behaviour of beam and particle is studied. The equation of motion of the particle is added to the system of the beam dynamic equations and an additional unknown representing the coordinate of the curvilinear path of the particle is introduced. The specially designed finite-element formulation of the three-dimensional beam based on the weak form of consistency conditions is employed where only the boundary conditions are affected by the contact forces.

[Suicide and evaluation. Review of French tools: Non-dimensional approach and self-assessment].

PubMed

Ducher, J-L; de Chazeron, I; Llorca, P-M

2016-06-01

Suicide prevention represents a major challenge to public health, and the suicide risk is a permanent concern in psychiatry. But the main difficulty is its diagnosis. What resources are available in French which seem to help therapists in this process? We can distinguish the non-dimensional approach, the use of self-administered questionnaires or interviewer-administrated questionnaires. In this paper, for reasons of editing constraints, we are interested only in a non-dimensional approach and direct assessment measures by self-assessment, analysing the strengths and limitations of each and taking into account scientific studies that have been devoted to them and their clinical relevance. We first considered various aspects of non-dimensional approach through suicidal risk factors research, suicidal emergency and suicidal potential concepts, Shea approach, the model of Mann and some recommended evaluations. This type of approach has a number of advantages, but also limitations. Dimensional approach allows going further. In this article, we also discuss the existing self-assessment tools in French as for example dedicated item for Beck Depression Inventory (BDI) or specific scales such as Reasons for Living Inventory (RFL), Suicidal Probability Scale (SPS), Beck Hopelessness Scale (BHS) and self-administered Suicide Risk Assessment Scale of Ducher (aRSD). These last two seem to be used as a priority regarding result of their validation studies. The strong correlation between the self-administered questionnaire aRSD and the interviewer-administered Suicide Risk Assessment Scale of Ducher RSD (r=0.92; P<10(-7)) shows the ability of patients to express their suicidal ideation if we want to invite them to do so. Copyright © 2015 L'Encéphale, Paris. Published by Elsevier Masson SAS. All rights reserved.

A two-dimensional ZnII coordination polymer constructed from benzene-1,2,3-tricarboxylic acid and N,N'-bis[(pyridin-4-yl)methylidene]hydrazine.

PubMed

Wang, Xiangfei; Yang, Fang; Tang, Meng; Yuan, Limin; Liu, Wenlong

2015-07-01

The hydrothermal synthesis of the novel complex poly[aqua(μ4-benzene-1,2,3-tricarboxylato)[μ2-4,4'-(hydrazine-1,2-diylidenedimethanylylidene)dipyridine](μ3-hydroxido)dizinc(II)], [Zn(C9H3O6)(OH)(C12H10N4)(H2O)]n, is described. The benzene-1,2,3-tricarboxylate ligand connects neighbouring Zn4(OH)2 secondary building units (SBUs) producing an infinite one-dimensional chain. Adjacent one-dimensional chains are connected by the N,N'-bis[(pyridin-4-yl)methylidene]hydrazine ligand, forming a two-dimensional layered structure. Adjacent layers are stacked to generate a three-dimensional supramolecular architecture via O-H...O hydrogen-bond interactions. The thermal stability of this complex is described and the complex also appears to have potential for application as a luminescent material.

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local Couplings

NASA Astrophysics Data System (ADS)

Große, Johannes

2007-11-01

This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, in a second part the conformal anomaly of four dimensional supersymmetric quantum field theories coupled to classical N=1 supergravity is explored in a superfield formulation. The complete basis for the anomaly and consistency conditions, which arise from cohomological considerations, are given. Possible implications for an extension of Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field theories are discussed.

COSMOS-e'-soft Higgsotic attractors

NASA Astrophysics Data System (ADS)

Choudhury, Sayantan

2017-07-01

In this work, we have developed an elegant algorithm to study the cosmological consequences from a huge class of quantum field theories (i.e. superstring theory, supergravity, extra dimensional theory, modified gravity, etc.), which are equivalently described by soft attractors in the effective field theory framework. In this description we have restricted our analysis for two scalar fields - dilaton and Higgsotic fields minimally coupled with Einstein gravity, which can be generalized for any arbitrary number of scalar field contents with generalized non-canonical and non-minimal interactions. We have explicitly used R^2 gravity, from which we have studied the attractor and non-attractor phases by exactly computing two point, three point and four point correlation functions from scalar fluctuations using the In-In (Schwinger-Keldysh) and the δ N formalisms. We have also presented theoretical bounds on the amplitude, tilt and running of the primordial power spectrum, various shapes (equilateral, squeezed, folded kite or counter-collinear) of the amplitude as obtained from three and four point scalar functions, which are consistent with observed data. Also the results from two point tensor fluctuations and the field excursion formula are explicitly presented for the attractor and non-attractor phase. Further, reheating constraints, scale dependent behavior of the couplings and the dynamical solution for the dilaton and Higgsotic fields are also presented. New sets of consistency relations between two, three and four point observables are also presented, which shows significant deviation from canonical slow-roll models. Additionally, three possible theoretical proposals have presented to overcome the tachyonic instability at the time of late time acceleration. Finally, we have also provided the bulk interpretation from the three and four point scalar correlation functions for completeness.

Cosmological rotating black holes in five-dimensional fake supergravity

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

Nozawa, Masato; Maeda, Kei-ichi; Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555

2011-01-15

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order 'Killing spinor'more » equation in 'fake supergravity' coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial 'Killing spinor', which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.« less

Modeling electron fractionalization with unconventional Fock spaces.

PubMed

Cobanera, Emilio

2017-08-02

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.

Thermal Investigation of Three-Dimensional GaN-on-SiC High Electron Mobility Transistors

DTIC Science & Technology

2017-07-01

AFRL-RY-WP-TR-2017-0143 THERMAL INVESTIGATION OF THREE- DIMENSIONAL GaN-on-SiC HIGH ELECTRON MOBILITY TRANSISTORS Qing Hao The University of Arizona...To) July 2017 Final 08 April 2015 – 10 April 2017 4. TITLE AND SUBTITLE THERMAL INVESTIGATION OF THREE-DIMENSIONAL GaN-on-SiC HIGH ELECTRON MOBILITY...used in many DoD applications, including integrated radio frequency (RF) amplifiers and power electronics . However, inherent inefficiencies in

Santiago Ramón y Cajal and three-dimensional cinema.

PubMed

Santarén, Juan Fernández

2015-01-01

In this article, I present and comment on two unpublished letters written by the Spanish engineer Carlos Mendizábal Brunet to Santiago Ramón y Cajal informing him of the development of a new device for three-dimensional cinema and asking for his approval. Fortunately, the answers given by Cajal to these two letters have also been preserved, and they reveal his interest in three-dimensional cinema; in the letters, he reported that he himself had designed a prototype capable of creating on a screen a feeling of 3-D relief, a subject about which he was always passionate.

SU(N ) fermions in a one-dimensional harmonic trap

NASA Astrophysics Data System (ADS)

Laird, E. K.; Shi, Z.-Y.; Parish, M. M.; Levinsen, J.

2017-09-01

We conduct a theoretical study of SU (N ) fermions confined by a one-dimensional harmonic potential. First, we introduce a numerical approach for solving the trapped interacting few-body problem, by which one may obtain accurate energy spectra across the full range of interaction strengths. In the strong-coupling limit, we map the SU (N ) Hamiltonian to a spin-chain model. We then show that an existing, extremely accurate ansatz—derived for a Heisenberg SU(2) spin chain—is extendable to these N -component systems. Lastly, we consider balanced SU (N ) Fermi gases that have an equal number of particles in each spin state for N =2 ,3 ,4 . In the weak- and strong-coupling regimes, we find that the ground-state energies rapidly converge to their expected values in the thermodynamic limit with increasing atom number. This suggests that the many-body energetics of N -component fermions may be accurately inferred from the corresponding few-body systems of N distinguishable particles.

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

NASA Astrophysics Data System (ADS)

Mylonas, Dionysios; Schupp, Peter; Szabo, Richard J.

2014-12-01

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

Black hole mining in the RST model

NASA Astrophysics Data System (ADS)

Basavaraju, Rohitvarma; Lowe, David A.

2017-06-01

We consider the possibility of mining black holes in the 1  +  1-dimensional dilaton gravity model of Russo, Susskind and Thorlacius. The model correctly incorporates Hawking radiation and back-reaction in a semiclassical expansion in 1/N, where N is the number of matter species. It is shown that the lifetime of a perturbed black hole is independent of the addition of any extra apparatus when realized by an arbitrary positive energy matter source. We conclude that mining does not occur in the RST model and comment on the implications of this for the black hole information paradox.

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.

N = 1 Deformations and RG flows of N = 2 SCFTs, part II: non-principal deformations

DOE PAGES

Agarwal, Prarit; Maruyoshi, Kazunobu; Song, Jaewon

2016-12-20

We continue to investigate the N = 1 deformations of four-dimensional N = 2 superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry [1]. This triggers a renormalization group (RG) flow to an N = 1 SCFT. We systematically analyze all possible deformations of this type for certain classes of N = 2 SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the E 6 SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to N = 2 at the end point of the RG flow. Most notably, we find that the SU(N)more » and Sp(N) conformal SQCDs can be deformed to flow to the Argyres-Douglas (AD) theories of type (A 1,D 2 N-1) and (A 1,D 2 N) respectively. This RG flow therefore allows us to compute the full superconformal index of the (A 1,D N) class of AD theories. Moreover, we find an infrared duality between N = 1 theories where the fixed point is described by an N = 2 AD theory. We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra.« less

N = 1 Deformations and RG flows of N = 2 SCFTs, part II: non-principal deformations

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

Agarwal, Prarit; Maruyoshi, Kazunobu; Song, Jaewon

We continue to investigate the N = 1 deformations of four-dimensional N = 2 superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry [1]. This triggers a renormalization group (RG) flow to an N = 1 SCFT. We systematically analyze all possible deformations of this type for certain classes of N = 2 SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the E 6 SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to N = 2 at the end point of the RG flow. Most notably, we find that the SU(N)more » and Sp(N) conformal SQCDs can be deformed to flow to the Argyres-Douglas (AD) theories of type (A 1,D 2 N-1) and (A 1,D 2 N) respectively. This RG flow therefore allows us to compute the full superconformal index of the (A 1,D N) class of AD theories. Moreover, we find an infrared duality between N = 1 theories where the fixed point is described by an N = 2 AD theory. We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra.« less

Rigid supersymmetric backgrounds of 3-dimensional Newton-Cartan supergravity

DOE PAGES

Knodel, Gino; Lisbao, Pedro; Liu, James T.

2016-06-06

Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the c → ∞ limit of three dimensional N = 2 super-gravity [1]. Here in the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there aremore » $$\\frac{1}{2}$$ -BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of N = 2 supergravity are connected to the solutions found here in the c → ∞ limit.« less

Bianchi's Bäcklund transformation for higher dimensional quadrics

NASA Astrophysics Data System (ADS)

Dincă, Ion I.

2016-12-01

deformations of general quadrics was on; it ended with Bianchi's discovery [1] from 1906 of the Bäcklund transformation for quadrics and the isometric correspondence provided by the Ivory affine transformation.In what concerns isometric deformations of higher dimensional non-degenerate quadrics the first result is that of Cartan's: in 1919-1920 Cartan has shown in [2], using mostly projective arguments and his exterior differential systems in involution and exteriorly orthogonal forms tools, that space forms of dimension n admit rich families of isometric deformations in surrounding space forms of dimension 2 n - 1, depending on n(n - 1) functions of one variable, that such isometric deformations admit lines of curvature given by a canonical form of exteriorly orthogonal forms and that the codimension n - 1 cannot be lowered without obtaining rigidity as the isometric deformation being the defining quadric. Because these isometric deformations admit lines of curvature they have flat normal bundle. Since the lines of curvature on n-dimensional space forms, when they are considered by definition as quadrics in surrounding (n + 1) -dimensional space forms, are undetermined, the lines of curvature on the isometric deformation and their corresponding curves on the quadric provide the common conjugate system (that is the second fundamental form is diagonal).From Cartan's papers until 1979 no further progress had been made in the isometric deformation problem for higher dimensional quadrics.In 1979, upon a suggestion from S.S. Chern and using Chebyshev coordinates on Hn(R) , which by the Cartan-Moore Theorem are lines of curvature and thus in bijective correspondence with isometric deformations of Hn(R) in R 2 n - 1, Tenenblat-Terng have developed in [3] the Bäcklund transformation of Hn(R) in R 2 n - 1 and Terng in [4] has developed the Bianchi Permutability Theorem for this Bäcklund transformation.In 1983 Berger, Bryant and Griffiths [5

Boundaries, mirror symmetry, and symplectic duality in 3d N = 4 gauge theory

DOE PAGES

Bullimore, Mathew; Dimofte, Tudor; Gaiotto, Davide; ...

2016-10-20

We introduce several families of N = (2, 2) UV boundary conditions in 3d N=4 gauge theories and study their IR images in sigma-models to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV boundary condition defines a pair of modules for quantized algebras of chiral Higgs- and Coulomb-branch operators, respectively, whose structure we derive. In the case of abelian theories, we use the formalism of hyperplane arrangements to make our constructions very explicit, and construct a half-BPS interface that implements the action of 3d mirror symmetry on gauge theories and boundary conditions. Finally, by studyingmore » two-dimensional compactifications of 3d N = 4 gauge theories and their boundary conditions, we propose a physical origin for symplectic duality $-$ an equivalence of categories of modules associated to families of Higgs and Coulomb branches that has recently appeared in the mathematics literature, and generalizes classic results on Koszul duality in geometric representation theory. We make several predictions about the structure of symplectic duality, and identify Koszul duality as a special case of wall crossing.« less

The massive fermion phase for the U(N) Chern-Simons gauge theory in D=3 at large N

DOE PAGES

Bardeen, William A.

2014-10-07

We explore the phase structure of fermions in the U(N) Chern-Simons Gauge theory in three dimensions using the large N limit where N is the number of colors and the fermions are taken to be in the fundamental representation of the U(N) gauge group. In the large N limit, the theory retains its classical conformal behavior and considerable attention has been paid to possible AdS/CFT dualities of the theory in the conformal phase. In this paper we present a solution for the massive phase of the fermion theory that is exact to the leading order of ‘t Hooft’s large Nmore » expansion. We present evidence for the spontaneous breaking of the exact scale symmetry and analyze the properties of the dilaton that appears as the Goldstone boson of scale symmetry breaking.« less

Description of the heterotic string solutions in U(N) supersymmetric QCD

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

Bolokhov, P. A.; Theoretical Physics Department, St. Petersburg State University, Ulyanovskaya 1, Peterhof, St. Petersburg, 198504; Shifman, M.

2009-04-15

We continue the study of heterotic non-Abelian Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings). Previously, such solutions were obtained [M. Shifman and A. Yung, Phys. Rev. D 77, 125016 (2008).] in a particular U(2) gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Here we generalize the previous results to U(N) gauge theories. As was suggested by Edalati and Tong [M. Edalati and D. Tong, J. High Energy Phys. 05 (2007) 005.], the string world-sheet theory is a heterotic N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extramore » right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) world-sheet model directly from the U(N) bulk theory. Parameters of the bulk theory are related to those of the world-sheet theory. Qualitatively this relation turns out to be the same as in the U(2) case.« less

Heterotic flux tubes in N=2 supersymmetric QCD with N=1 preserving deformations

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

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

2008-06-15

We consider non-Abelian Bogomol'nyi-Prasad-Sommerfield-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that world sheet supersymmetry is accidentally enhanced due to the facts that N=(1,1) supersymmetry is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1)xC rather than CP(N-1). This allowed them to suggest a heterotic N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields andmore » an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) world sheet model directly from the bulk theory. The relation between the bulk and world sheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the world sheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.« less

Full characterization of modular values for finite-dimensional systems

NASA Astrophysics Data System (ADS)

Ho, Le Bin; Imoto, Nobuyuki

2016-06-01

Kedem and Vaidman obtained a relationship between the spin-operator modular value and its weak value for specific coupling strengths [14]. Here we give a general expression for the modular value in the n-dimensional Hilbert space using the weak values up to (n - 1)th order of an arbitrary observable for any coupling strength, assuming non-degenerated eigenvalues. For two-dimensional case, it shows a linear relationship between the weak value and the modular value. We also relate the modular value of the sum of observables to the weak value of their product.

Non-Dimensional Formulation of Ventricular Work-Load Severity Under Concomitant Heart Valve Disease

NASA Astrophysics Data System (ADS)

Dong, Melody; Simon-Walker, Rachael; Dasi, Lakshmi

2012-11-01

Current guidelines on assessing the severity of heart valve disease rely on dimensional disease specific measures and are thus unable to capture severity under a concomitant heart valve disease scenario. Experiments were conducted to measure ventricular work-load in an in-house in-vitro left heart simulator. In-house tri-leaflet heart valves were built and parameterized to model concomitant heart valve disease. Measured ventricular power varied non-linearly with cardiac output and mean aortic pressure. Significant data collapse could be achieved by the non-dimensionalization of ventricular power with cardiac output, fluid density, and a length scale. The dimensionless power, Circulation Energy Dissipation Index (CEDI), indicates that concomitant conditions require a significant increase in the amount of work needed to sustain cardiac function. It predicts severity without the need to quantify individual disease severities. This indicates the need for new fluid-dynamics similitude based clinical guidelines to assist patients with multiple heart valve diseases. Funded by the American Heart Association.

Anisotropic carrier mobility in buckled two-dimensional GaN.

PubMed

Tong, Lijia; He, Junjie; Yang, Min; Chen, Zheng; Zhang, Jing; Lu, Yanli; Zhao, Ziyuan

2017-08-30

Developing nanoelectronic engineering requires two-dimensional (2d) materials with both usable carrier mobility and proper large band-gap. In this study, we present a detailed theoretical investigation of the intrinsic carrier mobilities of buckled 2d GaN. This buckled 2d GaN is accessed by hydrofluorination (FGaNH) and hydrogenation (HGaNH). We predict that the anisotropic carrier mobilities of buckled 2d GaN can exceed those of 2d MoS 2 and can be altered by an alterable surface chemical bond (convert from a Ga-F-Ga bond of FGaNH to a Ga-H bond of HGaNH). Moreover, converting FGaNH to HGaNH can significantly suppress hole mobility (even close to zero) and result in a transition from a p-type-like semiconductor (FGaNH) to an n-type-like semiconductor (HGaNH). These features make buckled 2d GaN a promising candidate for application in future conductivity-adjustable electronics.

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.

Band offsets of non-polar A-plane GaN/AlN and AlN/GaN heterostructures measured by X-ray photoemission spectroscopy.

PubMed

Sang, Ling; Zhu, Qin Sheng; Yang, Shao Yan; Liu, Gui Peng; Li, Hui Jie; Wei, Hong Yuan; Jiao, Chun Mei; Liu, Shu Man; Wang, Zhan Guo; Zhou, Xiao Wei; Mao, Wei; Hao, Yue; Shen, Bo

2014-01-01

The band offsets of non-polar A-plane GaN/AlN and AlN/GaN heterojunctions are measured by X-ray photoemission spectroscopy. A large forward-backward asymmetry is observed in the non-polar GaN/AlN and AlN/GaN heterojunctions. The valence-band offsets in the non-polar A-plane GaN/AlN and AlN/GaN heterojunctions are determined to be 1.33 ± 0.16 and 0.73 ± 0.16 eV, respectively. The large valence-band offset difference of 0.6 eV between the non-polar GaN/AlN and AlN/GaN heterojunctions is considered to be due to piezoelectric strain effect in the non-polar heterojunction overlayers.

Negative differential resistance observed from vertical p+-n+ junction device with two-dimensional black phosphorous

NASA Astrophysics Data System (ADS)

Lee, Daeyeong; Jang, Young Dae; Kweon, Jaehwan; Ryu, Jungjin; Hwang, Euyheon; Yoo, Won Jong; Samsung-SKKU Graphene/2D Center (SSGC) Collaboration

A vertical p+-n+ homojunction was fabricated by using black phosphorus (BP) as a van der Waals two-dimensional (2D) material. The top and bottom layers of the materials were doped by chemical dopants of gold chloride (AuCl3) for p-type doping and benzyl viologen (BV) for n-type doping. The negative differential resistance (NDR) effect was clearly observed from the output curves of the fabricated BP vertical devices. The thickness range of the 2D material showing NDR and the peak to valley current ratio of NDR are found to be strongly dependent on doping condition, gate voltage, and BP's degradation level. Furthermore, the carrier transport of the p+-n+ junction was simulated by using density functional theory (DFT) and non-equilibrium Green's function (NEGF). Both the experimental and simulation results confirmed that the NDR is attributed to the band-to-band tunneling (BTBT) across the 2D BP p+-n+ junction, and further quantitative details on the carrier transport in the vertical p+-n+ junction devices were explored, according to the analyses of the measured transfer curves and the DFT simulation results. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2013R1A2A2A01015516).

Quantum return probability of a system of N non-interacting lattice fermions

NASA Astrophysics Data System (ADS)

Krapivsky, P. L.; Luck, J. M.; Mallick, K.

2018-02-01

We consider N non-interacting fermions performing continuous-time quantum walks on a one-dimensional lattice. The system is launched from a most compact configuration where the fermions occupy neighboring sites. We calculate exactly the quantum return probability (sometimes referred to as the Loschmidt echo) of observing the very same compact state at a later time t. Remarkably, this probability depends on the parity of the fermion number—it decays as a power of time for even N, while for odd N it exhibits periodic oscillations modulated by a decaying power law. The exponent also slightly depends on the parity of N, and is roughly twice smaller than what it would be in the continuum limit. We also consider the same problem, and obtain similar results, in the presence of an impenetrable wall at the origin constraining the particles to remain on the positive half-line. We derive closed-form expressions for the amplitudes of the power-law decay of the return probability in all cases. The key point in the derivation is the use of Mehta integrals, which are limiting cases of the Selberg integral.

Collective charge excitations of the two-dimensional electride Ca2N

NASA Astrophysics Data System (ADS)

Cudazzo, Pierluigi; Gatti, Matteo

2017-09-01

Ca2N is a layered material that has been recently identified as a two-dimensional (2D) electride, an unusual ionic compound in which electrons serve as anions. The electronic properties of 2D electrides attract considerable interest as the anionic electrons, which form a 2D layer sandwiched between atomic planes, are highly mobile as they are not attached to any ion. Here, on the basis of first-principles time-dependent density-functional theory calculations, we investigate the collective excitations of the electrons—i.e., the plasmons—in Ca2N as a function of wave vector q . Our calculations reveal an intrinsic negative in-plane dispersion of the anionic plasmon, in striking contrast with the homogeneous electron gas. Moreover, for wave vectors q normal to the planes, we find a long-lived plasmon that continues to exist well beyond the first Brillouin zone. This is a mark of the electronic inhomogeneities in the charge response that Ca2N shares with other layered materials like transition-metal dichalcogenides and MgB2. Finally, we compare the plasmon properties of Ca2N in its bulk and monolayer forms, which shows the effect of the different electronic structures and dimensionalities.

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.

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.

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.

Robust ferroelectricity in two-dimensional SbN and BiP.

PubMed

Liu, Chang; Wan, Wenhui; Ma, Jie; Guo, Wei; Yao, Yugui

2018-05-03

Based on first-principles calculations, we discover two new two-dimensional (2D) ferroelectric materials SbN and BiP. Both of them are stable in a phosphorene-like structure and maintain their ferroelectricity above room temperature. Till date, SbN has the largest in-plane spontaneous polarization of about 7.81 × 10-10 C m-1 ever found in 2D ferroelectric materials, and it can retain its ferroelectricity until melting at about 1700 K. The spontaneous polarizations and switching barriers can easily be tuned by strains. Additionally, the ferroelectricity can still be maintained in their multilayers. These advantages make SbN and BiP promising candidate materials for future integrated ferroelectric devices.

Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting.

PubMed

Chen, Leiming; Lee, Chiu Fan; Toner, John

2016-07-25

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.

Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting

NASA Astrophysics Data System (ADS)

Chen, Leiming; Lee, Chiu Fan; Toner, John

2016-07-01

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems: two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent ζ and the roughness exponents χx,y that characterize these correlations.

Period and amplitude of non-volcanic tremors and repeaters: a dimensional analysis

NASA Astrophysics Data System (ADS)

Nielsen, Stefan

2017-04-01

Since its relatively recent discovery, the origin of non-volcanic tremor has been source of great curiosity and debate. Two main interpretations have been proposed, one based on fluid migration, the other relating to slow slip events on a plate boundary (the latter hypothesis has recently gained considerable ground). Here I define the conditions of slip of one or more small asperities embedded within a larger creeping fault patch. The radiation-damping equation coupled with rate-and-state friction evolution equations results in a system of ordinary differential equations. For a finite size asperity, the system equates to a peculiar non-linear damped oscillator, converging to a limit cycle. Dimensional analysis shows that period and amplitude of the oscillations depend on dimensional parameter combinations formed from a limited set of parameters: asperity dimension Γ, rate and state friction parameters (a, b, L), shear stiffness of the medium G, mass density ρ, background creep rate ˙V and normal stress σ. Under realistic parameter ranges, the asperity may show (1) tremor-like short period oscillations, accelerating to radiate sufficient energy to be barely detectable and a periodicity of the order of one to ten Hertz, as observed for non-volcanic tremor activity at the base of large inter-plate faults; (2) isolated stick-slip events with intervals in the order of days to months, as observed in repeater events of modest magnitude within creeping fault sections.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

PubMed

Kong, Shengchun; Nan, Bin

2014-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

PubMed Central

Kong, Shengchun; Nan, Bin

2013-01-01

We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

Epitaxy of advanced nanowire quantum devices

NASA Astrophysics Data System (ADS)

Gazibegovic, Sasa; Car, Diana; Zhang, Hao; Balk, Stijn C.; Logan, John A.; de Moor, Michiel W. A.; Cassidy, Maja C.; Schmits, Rudi; Xu, Di; Wang, Guanzhong; Krogstrup, Peter; Op Het Veld, Roy L. M.; Zuo, Kun; Vos, Yoram; Shen, Jie; Bouman, Daniël; Shojaei, Borzoyeh; Pennachio, Daniel; Lee, Joon Sue; van Veldhoven, Petrus J.; Koelling, Sebastian; Verheijen, Marcel A.; Kouwenhoven, Leo P.; Palmstrøm, Chris J.; Bakkers, Erik P. A. M.

2017-08-01

Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin-orbit coupling is brought into contact with a superconductor. To exploit the potential of non-Abelian anyons—which are key elements of topological quantum computing—fully, they need to be exchanged in a well-controlled braiding operation. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor-semiconductor interface. Quantum transport measurements of nanowire ‘hashtags’ reveal Aharonov-Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin-orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor-semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.

An exact conformal symmetry Ansatz on Kaluza-Klein reduced TMG

NASA Astrophysics Data System (ADS)

Moutsopoulos, George; Ritter, Patricia

2011-11-01

Using a Kaluza-Klein dimensional reduction, and further imposing a conformal Killing symmetry on the reduced metric generated by the dilaton, we show an Ansatz that yields many of the known stationary axisymmetric solutions to TMG.

U-folds as K3 fibrations

NASA Astrophysics Data System (ADS)

Braun, Andreas P.; Fucito, Francesco; Morales, Jose Francisco

2013-10-01

We study four-dimensional flux vacua describing intrinsic non- perturbative systems of 3 and 7 branes in type IIB string theory. The solutions are described as compactifications of a G(ravity) theory on a Calabi Yau threefold which consists of a fibration of an auxiliary K3 surface over an S 2 base. In the spirit of F-theory, the complex structure of the K3 surface varying over the base codifies the details of the fluxes, the dilaton and the warp factors in type IIB string theory. We discuss in detail some simple examples of geometric and non-geometric solutions where the precise flux/geometry dictionary can be explicitly worked out. In particular, we describe non-geometric T-fold solutions exhibiting non-trivial T-duality monodromies exchanging 3- and 7-branes.

Ferroelectric polarization-controlled two-dimensional electron gas in ferroelectric/AlGaN/GaN heterostructure

NASA Astrophysics Data System (ADS)

Kong, Y. C.; Xue, F. S.; Zhou, J. J.; Li, L.; Chen, C.; Li, Y. R.

2009-06-01

The control effect of the ferroelectric polarization on the two-dimensional electron gas (2DEG) in a ferroelectric/AlGaN/GaN metal-ferroelectric-semiconductor (MFS) structure is theoretically analyzed by a self-consistent approach. With incorporating the hysteresis nature of the ferroelectric into calculation, the nature of the control effect is disclosed, where the 2DEG density is depleted/restored after poling/depoling operation on the MFS structure. The orientation of the ferroelectric polarization is clarified to be parallel to that of the AlGaN barrier, which, based on an electrostatics analysis, is attributed to the pinning effect of the underlying polarization. Reducing the thickness of the AlGaN barrier from 25 nm to 20 nm leads to an improved control modulation of the 2DEG density from 36.7% to 54.1%.

Two-dimensional Yukawa interactions from nonlocal Proca quantum electrodynamics

NASA Astrophysics Data System (ADS)

Alves, Van Sérgio; Macrı, Tommaso; Magalhães, Gabriel C.; Marino, E. C.; Nascimento, Leandro O.

2018-05-01

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3 +1 ) dimensions. Thereafter, we consider that the fermionic matter field propagates only in (2 +1 ) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2 +1 ) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudo quantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed.

(Super)symmetries of semiclassical models in theoretical and condensed matter physics

NASA Astrophysics Data System (ADS)

Ngome, J.-P.

2011-03-01

Van Holten's covariant algorithm for deriving conserved quantities is presented, with particular attention paid to Runge-Lenz-type vectors. The classical dynamics of isospin-carrying particles is reviewed. Physical applications including non-Abelian monopole-type systems in diatoms, introduced by Moody, Shapere and Wilczek, are considered. Applied to curved space, the formalism of van Holten allows us to describe the dynamical symmetries of generalized Kaluza-Klein monopoles. The framework is extended to supersymmetry and applied to the SUSY of the monopoles. Yet another application concerns the three-dimensional non-commutative oscillator.

A new spin on electron liquids: Phenomena in systems with spin-orbit coupling

NASA Astrophysics Data System (ADS)

Bernevig, B. Andrei

Conventional microelectronic devices are based on the ability to store and control the flow of electronic charge. Spin-based electronics promises a radical alternative, offering the possibility of logic operations with much lower power consumption than equivalent charge-based logic operations. Our research suggests that spin transport is fundamentally different from the transport of charge. The generalized Ohm's law that governs the flow of spins indicates that the generation of spin current by an electric field can be reversible and non-dissipative. Spin-orbit coupling and spin currents appear in many other seemingly unrelated areas of physics. Spin currents are as fundamental in theoretical physics as charge currents. In strongly correlated systems such as spin-chains, one can write down the Hamiltonian as a spin-current - spin-current interaction. The research presented here shows that the fractionalized excitations of one-dimensional spin chains are gapless and carry spin current. We present the most interesting example of such a chain, the Haldane-Shastry spin chain, which is exactly solvable in terms of real-space wavefunctions. Spin-orbit coupling can be found in high-energy physics, hidden under a different name: non-trivial fibrations. Particles moving in a space which is non-trivially related to an (iso)spin space acquire a gauge connection (the condensed-matter equivalent of a Berry phase) which can be either abelian or non-abelian. In most cases, the consequences of such gauge connection are far-reaching. We present a problem where particles move on an 8-dimensional manifold and posses an isospin space with is a 7-sphere S 7. The non-trivial isospin space gives the Hamiltonian SO (8) landau-level structure, and the system exhibits a higher-dimensional Quantum Hall Effect.

Strong Coupling Gauge Theories in LHC ERA

NASA Astrophysics Data System (ADS)

Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.

2011-01-01

conformal Higgs / Kazumoto Haba, Shinya Matsuzaki and Koichi Yamawaki -- Phase structure of topologically massive gauge theory with fermion / Yuichi Hoshino -- New regularization in extra dimensional model and renormalization group flow of the cosmological constant / Shoichi Ichinose -- Spectral analysis of dense two-color QCD / T. Kanazawa, T. Wettig and N. Yamamoto -- NJL model with dimensional regularization at finite temperature / T. Fujihara ... [et al.] -- A new method of evaluating the dynamical chiral symmetry breaking scale and the chiral restoration temperature in general gauge theories by using the non-perturbative renormalization group analyses with general 4-Fermi effective interaction space / Ken-Ichi Aoki, Daisuke Sato and Kazuhiro Miyashita -- The effective chiral Lagrangian with vector mesons and hadronic [symbol] decays / D. Kimura ... [et al.] -- Spontaneous SUSY breaking with anomalous U(1) symmetry in metastable vacua and moduli stabilization / Hiroyuki Nishino -- A new description of the lattice Yang-Mills theory and non-abelian magnetic monopole dominance in the string tension / Akihiro Shibata -- Thermodynamics with unbroken center symmetry in two-flavor QCD / S. Takemoto, M. Harada and C. Sasaki -- Masses of vector bosons in two-color QCD based on the hidden local symmetry / T. Yamaoka, M. Harada and C. Nonaka -- Walking dynamics from string duals / Maurizio Piai -- The quark mass dependence of the nucleon mass in AdS/QCD / Hyo Chul Ahn -- Structure of thermal quasi-fermion in QED/QCD from the Dyson-Schwinger equation / Hisao Nakkagawa -- Critical behaviors of sigma-mode and pion in holographic superconductors / Cheonsoo Park.

(3+1)-Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

NASA Astrophysics Data System (ADS)

Kumar, R.; Mukhopadhyay, Debmalya

2018-06-01

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations corresponding to the combined "scalar" and "vector" gauge symmetry transformations for the (3+1)-dimensional (4D) topologically massive non-Abelian (B \\wedge F) theory with the help of geometrical superfield formalism. For this purpose, we use three horizontality conditions (HCs). The first HC produces the (anti-)BRST transformations for the 1-form gauge field and corresponding (anti-)ghost fields whereas the second HC yields the (anti-)BRST transformations for 2-form field and associated (anti-)ghost fields. The integrability of second HC produces third HC. The latter HC produces the (anti-)BRST symmetry transformations for the compensating auxiliary vector field and corresponding ghosts. We obtain five (anti-)BRST invariant Curci-Ferrari (CF)-type conditions which emerge very naturally as the off-shoots of superfield formalism. Out of five CF-type conditions, two are fermionic in nature. These CF-type conditions play a decisive role in providing the absolute anticommutativity of the (anti-)BRST transformations and also responsible for the derivation of coupled but equivalent (anti-)BRST invariant Lagrangian densities. Furthermore, we capture the (anti-)BRST invariance of the coupled Lagrangian densities in terms of the superfields and translation generators along the Grassmannian directions θ and \\bar{θ }.

Solitons and black holes in non-Abelian Einstein-Born-Infeld theory

NASA Astrophysics Data System (ADS)

Dyadichev, V. V.; Gal'tsov, D. V.

2000-08-01

Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.

Prediction of a two-dimensional S3N2 solid for optoelectronic applications

NASA Astrophysics Data System (ADS)

Xiao, Hang; Shi, Xiaoyang; Liao, Xiangbiao; Zhang, Yayun; Chen, Xi

2018-02-01

Two-dimensional materials have attracted tremendous attention for their fascinating electronic, optical, chemical, and mechanical properties. However, the band gaps of most reported two-dimensional (2D) materials are smaller than 2.0 eV, which has greatly restricted their optoelectronic applications in the blue and ultraviolet range of the spectrum. Here, we propose a stable trisulfur dinitride (S3N2 ) 2D crystal that is a covalent network composed solely of S-N σ bonds. The S3N2 crystal is dynamically, thermally, and chemically stable, as confirmed by the computed phonon spectrum and ab initio molecular dynamics simulations. GW calculations show that the S3N2 crystal is a wide, direct band-gap (3.92 eV) semiconductor with a small-hole effective mass. In addition, the band gap of S3N2 structures can be tuned by forming multilayer S3N2 crystals, S3N2 nanoribbons, and S3N2 nanotubes, expanding its potential applications. The anisotropic optical response of the 2D S3N2 crystal is revealed by GW-Bethe-Salpeter-equation calculations. The optical band gap of S3N2 is 2.73 eV and the exciton binding energy of S3N2 is 1.19 eV, showing a strong excitonic effect. Our result not only marks the prediction of a 2D crystal composed of nitrogen and sulfur, but also underpins potential innovations in 2D electronics and optoelectronics.

Application of N-Doped Three-Dimensional Reduced Graphene Oxide Aerogel to Thin Film Loudspeaker.

PubMed

Kim, Choong Sun; Lee, Kyung Eun; Lee, Jung-Min; Kim, Sang Ouk; Cho, Byung Jin; Choi, Jung-Woo

2016-08-31

We built a thermoacoustic loudspeaker employing N-doped three-dimensional reduced graphene oxide aerogel (N-rGOA) based on a simple template-free fabrication method. A two-step fabrication process, which includes freeze-drying and reduction/doping, was used to realize a three-dimensional, freestanding, and porous graphene-based loudspeaker, whose macroscopic structure can be easily modulated. The simplified fabrication process also allows the control of structural properties of the N-rGOAs, including density and area. Taking advantage of the facile fabrication process, we fabricated and analyzed thermoacoustic loudspeakers with different structural properties. The anlayses showed that a N-rGOA with lower density and larger area can produce a higher sound pressure level (SPL). Furthermore, the resistance of the proposed loudspeaker can be easily controlled through heteroatom doping, thereby helping to generate higher SPL per unit driving voltage. Our success in constructing an array of optimized N-rGOAs able to withstand input power as high as 40 W demonstrates that a practical thermoacoustic loudspeaker can be fabricated using the proposed mass-producible solution-based process.

N =2 super Yang-Mills theory in projective superspace

NASA Astrophysics Data System (ADS)

Davgadorj, Ariunzul; von Unge, Rikard

2018-05-01

We find a formulation of N =2 supersymmetric Yang-Mills theory in projective superspace. In particular we find an expression for the field strength in terms of an unconstrained prepotential which is desirable when quantizing the theory. We use this to write the action in terms of the prepotential and show that it reduces to the known result in the Abelian limit.

Differential Laser Doppler based Non-Contact Sensor for Dimensional Inspection with Error Propagation Evaluation

PubMed Central

Mekid, Samir; Vacharanukul, Ketsaya

2006-01-01

To achieve dynamic error compensation in CNC machine tools, a non-contact laser probe capable of dimensional measurement of a workpiece while it is being machined has been developed and presented in this paper. The measurements are automatically fed back to the machine controller for intelligent error compensations. Based on a well resolved laser Doppler technique and real time data acquisition, the probe delivers a very promising dimensional accuracy at few microns over a range of 100 mm. The developed optical measuring apparatus employs a differential laser Doppler arrangement allowing acquisition of information from the workpiece surface. In addition, the measurements are traceable to standards of frequency allowing higher precision.

High-resolution non-destructive three-dimensional imaging of integrated circuits

NASA Astrophysics Data System (ADS)

Holler, Mirko; Guizar-Sicairos, Manuel; Tsai, Esther H. R.; Dinapoli, Roberto; Müller, Elisabeth; Bunk, Oliver; Raabe, Jörg; Aeppli, Gabriel

2017-03-01

Modern nanoelectronics has advanced to a point at which it is impossible to image entire devices and their interconnections non-destructively because of their small feature sizes and the complex three-dimensional structures resulting from their integration on a chip. This metrology gap implies a lack of direct feedback between design and manufacturing processes, and hampers quality control during production, shipment and use. Here we demonstrate that X-ray ptychography—a high-resolution coherent diffractive imaging technique—can create three-dimensional images of integrated circuits of known and unknown designs with a lateral resolution in all directions down to 14.6 nanometres. We obtained detailed device geometries and corresponding elemental maps, and show how the devices are integrated with each other to form the chip. Our experiments represent a major advance in chip inspection and reverse engineering over the traditional destructive electron microscopy and ion milling techniques. Foreseeable developments in X-ray sources, optics and detectors, as well as adoption of an instrument geometry optimized for planar rather than cylindrical samples, could lead to a thousand-fold increase in efficiency, with concomitant reductions in scan times and voxel sizes.

High-resolution non-destructive three-dimensional imaging of integrated circuits.

PubMed

Holler, Mirko; Guizar-Sicairos, Manuel; Tsai, Esther H R; Dinapoli, Roberto; Müller, Elisabeth; Bunk, Oliver; Raabe, Jörg; Aeppli, Gabriel

2017-03-15

Modern nanoelectronics has advanced to a point at which it is impossible to image entire devices and their interconnections non-destructively because of their small feature sizes and the complex three-dimensional structures resulting from their integration on a chip. This metrology gap implies a lack of direct feedback between design and manufacturing processes, and hampers quality control during production, shipment and use. Here we demonstrate that X-ray ptychography-a high-resolution coherent diffractive imaging technique-can create three-dimensional images of integrated circuits of known and unknown designs with a lateral resolution in all directions down to 14.6 nanometres. We obtained detailed device geometries and corresponding elemental maps, and show how the devices are integrated with each other to form the chip. Our experiments represent a major advance in chip inspection and reverse engineering over the traditional destructive electron microscopy and ion milling techniques. Foreseeable developments in X-ray sources, optics and detectors, as well as adoption of an instrument geometry optimized for planar rather than cylindrical samples, could lead to a thousand-fold increase in efficiency, with concomitant reductions in scan times and voxel sizes.

Exotic ferromagnetism in the two-dimensional quantum material C3N

NASA Astrophysics Data System (ADS)

Huang, Wen-Cheng; Li, Wei; Liu, Xiaosong

2018-04-01

The search for and study of exotic quantum states in novel low-dimensional quantum materials have triggered extensive research in recent years. Here, we systematically study the electronic and magnetic structures in the newly discovered two-dimensional quantum material C3N within the framework of density functional theory. The calculations demonstrate that C3N is an indirect-band semiconductor with an energy gap of 0.38 eV, which is in good agreement with experimental observations. Interestingly, we find van Hove singularities located at energies near the Fermi level, which is half that of graphene. Thus, the Fermi energy easily approaches that of the singularities, driving the system to ferromagnetism, under charge carrier injection, such as electric field gating or hydrogen doping. These findings not only demonstrate that the emergence of magnetism stems from the itinerant electron mechanism rather than the effects of local magnetic impurities, but also open a new avenue to designing field-effect transistor devices for possible realization of an insulator-ferromagnet transition by tuning an external electric field.