Non-Abelian family symmetries as portals to dark matter
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.; Fischer, O.
2016-01-01
Non-Abelian family symmetries offer a very promising explanation for the flavour structure in the Standard Model and its extensions. We explore the possibility that dark matter consists in fermions that transform under a family symmetry, such that the visible and dark sector are linked by the familons - Standard Model gauge singlet scalars, responsible for spontaneously breaking the family symmetry. We study three representative models with non-Abelian family symmetries that have been shown capable to explain the masses and mixing of the Standard Model fermions.
Black holes and Abelian symmetry breaking
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Niz, Gustavo; Tasinato, Gianmassimo
2016-09-01
Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector–tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector–tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.
Black holes and Abelian symmetry breaking
NASA Astrophysics Data System (ADS)
Chagoya, Javier; Niz, Gustavo; Tasinato, Gianmassimo
2016-09-01
Black hole configurations offer insights on the nonlinear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector-tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector-tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarisation, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.
On discrete symmetries for a whole Abelian model
NASA Astrophysics Data System (ADS)
Chauca, J.; Doria, R.
2012-10-01
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 {Dμ,Xiμ} and the physical basis {GμI}. 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 driven 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 {GμI} 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.
On discrete symmetries for a whole Abelian model
Chauca, J.; Doria, R.
2012-09-24
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 driven 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.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Non-Abelian discrete gauge symmetries in F-theory
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Pugh, Tom G.; Regalado, Diego
2016-02-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.
Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study
NASA Astrophysics Data System (ADS)
Zohar, Erez; Wahl, Thorsten B.; Burrello, Michele; Cirac, J. Ignacio
2016-11-01
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 a 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.
Abelian Floquet symmetry-protected topological phases in one dimension
NASA Astrophysics Data System (ADS)
Roy, Rahul; Harper, Fenner
2016-09-01
Time-dependent systems have recently been shown to support novel types of topological order that cannot be realized in static systems. In this paper we consider a range of time-dependent, interacting systems in one dimension that are protected by an Abelian symmetry group. We classify the distinct topological phases that can exist in this setting and find that they may be described by a bulk invariant associated with the unitary evolution of the closed system. In the open system, nontrivial phases correspond to the appearance of edge modes, which have signatures in the many-body quasienergy spectrum and which relate to the bulk invariant through a form of bulk-edge correspondence. We introduce simple models which realize nontrivial dynamical phases in a number of cases, and outline a loop construction that can be used to generate such phases more generally.
NASA Astrophysics Data System (ADS)
Mross, David F.; Essin, Andrew; Alicea, Jason; Stern, Ady
2016-01-01
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 Z4 parafermion zero modes.
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.
On abelian and discrete symmetries in F-theory
NASA Astrophysics Data System (ADS)
Piragua, Hernan Augusto
In this dissertation, we systematically construct and study global F-theory compactifications with abelian and discrete gauge groups. These constructions are of fundamental relevance for both conceptual and phenomenological reasons. In the case of abelian symmetries, we systematically engineer compactifications that support U(1)xU(1) and U(1)xU(1)xU(1) gauge groups. The engineered geometries are elliptic fibrations with Mordell-Weil group rank two and three respectively. The bases of the fibrations are arbitrary, but as proofs of concept, we explicit create examples with bases P 2 and P3. We study the low energy physics of these compactifications, we calculate the matter spectrum and confirm that it is anomaly free. In 4D compactifications, the G4 flux is designed and the existence of Yukawa couplings is verified. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. The discrete gauge groups Z3 and U(1) x Z2 are naturally found when P2 and P1 x P1 are used as fiber ambient spaces. We also find the first realization of matter with U(1) charge three. Finally, we study the discrete gauge group Z 3 in detail. We find the three elements of the Tate-Shafarevich (TS) group. We make use of the Higgs mechanism with the charge three hypermultiplets and the Kaluza-Klein reduction from 6D to 5D. The results are interpreted from the F- M- theory duality perspective. In F-theory, compactifications over any of the three elements of the TS groups yield the same low energy physics, however, M-theory compactifications over the same elements give rise to different
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. PMID:26849608
Breaking an Abelian gauge symmetry near a black hole horizon
Gubser, Steven S.
2008-09-15
I argue that coupling the Abelian Higgs model to gravity plus a negative cosmological constant leads to black holes which spontaneously break the gauge invariance via a charged scalar condensate slightly outside their horizon. This suggests that black holes can superconduct.
NASA Astrophysics Data System (ADS)
Ye, Peng; Gu, Zheng-Cheng
2016-05-01
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered state (or atomic insulator) as long as certain global symmetry G is unbroken. At low energies, most of the two-dimensional SPTs with Abelian symmetry can be described by topological quantum field theory (TQFT) of the multicomponent Chern-Simons type. However, in contrast to the fractional quantum Hall effect where TQFT can give rise to interesting bulk anyons, TQFT for SPTs only supports trivial bulk excitations. The essential question in TQFT descriptions for SPTs is to understand how the global symmetry is implemented in the partition function. In this paper, we systematically study TQFT of three-dimensional SPTs with unitary Abelian symmetry (e.g., ZN1×ZN2×... ). In addition to the usual multicomponent B F topological term at level-1, we find that there are new topological terms with quantized coefficients (e.g., a1∧a2∧d a2 and a1∧a2∧a3∧a4 ) in TQFT actions, where a1,a2,... are 1-form U(1) gauge fields. These additional topological terms cannot be adiabatically turned off as long as G is unbroken. By investigating symmetry transformations for the TQFT partition function, we end up with the classification of SPTs that is consistent with the well-known group cohomology approach. We also discuss how to gauge the global symmetry and possible TQFT descriptions of Dijkgraaf-Witten gauge theory.
NASA Astrophysics Data System (ADS)
von Keyserlingk, C. W.; Sondhi, S. L.
2016-06-01
Recent work suggests that a sharp definition of "phase of matter" can be given for some quantum systems out of equilibrium, first for many-body localized systems with time-independent Hamiltonians and more recently for periodically driven or Floquet localized systems. In this work, we propose a classification of the finite Abelian symmetry-protected phases of interacting Floquet localized systems in one dimension. We find that the different Floquet phases correspond to elements of ClG×AG , where ClG is the undriven interacting classification, and AG is a set of (twisted) one-dimensional representations corresponding to symmetry group G . We will address symmetry-broken phases in a subsequent paper C. W. von Keyserlingk and S. L. Sondhi, following paper, Phys. Rev. B 93, 245146 (2016), 10.1103/PhysRevB.93.245146.
Abelian gauge symmetries and proton decay in global F-theory GUTs
NASA Astrophysics Data System (ADS)
Grimm, Thomas W.; Weigand, Timo
2010-10-01
The existence of Abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau four-fold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine Abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) grand unified theory (GUT) models this mechanism enforces a global U(1)X symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau four-folds and their mirror duals starting from an underlying E8 and E7×U(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyze F-theory GUT models.
A topological semimetal model with f-wave symmetry in a non-Abelian triangular optical lattice
NASA Astrophysics Data System (ADS)
Li, Ling; Bai, Zhiming; Hao, Ningning; Liu, Guocai
2016-08-01
We demonstrate that an chiral f-wave topological semimetal can be induced in a non-Abelian triangular optical lattice. We show that the f-wave symmetry topological semimetal is characterized by the topological invariant, i.e., the winding number W, with W=3 and is different from the semimetal with W=1 and 2 which have the p-wave and d-wave symmetry, respectively.
Complementarity and Symmetry in Family Therapy Communication.
ERIC Educational Resources Information Center
Heatherington, Laurie; Friedlander, Myrna L.
1990-01-01
Examined relational control communication patterns in systemic family therapy sessions. Results from 29 families showed significantly more complementarity than symmetry. Neither complementarity nor symmetry was predictive of family members' perceptions of the therapeutic alliance as measured by Couple and Family Therapy Alliance Scales. (Author/NB)
Origin of Abelian gauge symmetries in heterotic/F-theory duality
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng
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
NASA Astrophysics Data System (ADS)
Gao, Ya-Jun
2006-01-01
The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein-Maxwell theory with p Abelian gauge fields (EM-p theory, for short). Two EHC structural Riemann-Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-p theory. This symmetry group is verified to have the structure of semidirect product of Kac-Moody group SU(hat p+1,1) and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.
Cosmoparticle physics of family symmetry breaking
NASA Astrophysics Data System (ADS)
Khlopov, Maxim Yu.
1993-07-01
The foundations of both particle theory and cosmology are hidden at super energy scale and can not be tested by direct laboratory means. Cosmoparticle physics is developed to probe these foundations by the proper combination of their indirect effects, thus providing definite conclusions on their reliability. Cosmological and astrophysical tests turn to be complementary to laboratory searches of rare processes, induced by new physics, as it can be seen in the case of gauge theory of broken symmetry of quark and lepton families, ascribing to the hierarchy of the horizontal symmetry breaking the observed hierarchy of masses and the mixing between quark and lepton families.
Scale-Setting Without the Higgs Mechanism:. Non-Abelian Symmetry
NASA Astrophysics Data System (ADS)
Anderson, J. T.
For the non-Abelian Higgs model it is shown that the coupled equations of motion for Aμ, ϕ and ϕ* have nonanalytic singularities which must be removed if the equations are integrable. Current conservation is found to remove the singularities in the vector-field equation and give a mass scale independent of V and the Higgs mechanism. The self-consistent field solutions for Aμ and the ϕ fields give either (1) the Higgs mechanism, zero current and the pure-gauge solution, or (2) nonzero current, a gauge-covariant solution and the mass scale independent of V and the Higgs mechanism.
Yao, Hong; Lee, Dung-Hai
2011-08-19
We introduce an exactly solvable SU(2)-invariant spin-1/2 model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits the spin quantum Hall effect with quantized spin Hall conductivity σ(xy)(s)=ℏ/2π, and that the spin response is effectively described by the SO(3) level-1 Chern-Simons theory at low energy. We further propose that a SU(2) level-2 Chern-Simons theory is the effective field theory describing the topological structure of the non-Abelian SU(2) invariant spin liquid.
Lepton Flavour Violation and electron EDM in SUSY with a non-abelian flavour symmetry
Calibbi, Lorenzo
2008-11-23
We present the lepton sector phenomenology of a supersymmetric flavour model based on a SU(3) horizontal symmetry. This model successfully reproduces the observed fermion masses and mixings, without introducing unacceptably large SUSY sources of flavour and CP violation. We show that the model, which is at present weakly constrained, predicts the electron EDM and {mu}{yields}e,y to be within the final sensitivity of the currently running experiments, at least for SUSY masses within the reach of the LHC.
Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries
NASA Astrophysics Data System (ADS)
Chen, Mu-Chun; Fallbacher, Maximilian; Omura, Yuji; Ratz, Michael; Staudt, Christian
2013-08-01
In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models.
Supersymmetric parameter space of family symmetries
Velasco-Sevilla, L.
2008-11-23
In this talk I have emphasized the effects of considering departures from the minimal flavour violation conditions, in the context of CMSSM-like theories, introduced by boundary conditions at GUT scale from Family Symmetries. In [1] we have shown the results of running these conditions down to EW, where constraints from fermion masses and CKM matrix elements have been used. Only when the expansion parameter in the sdown-squark sector is relatively large it is possible to relax the lower limit from b{yields}s{gamma} on the universal gaugino mass. The expansion parameter associated with the slepton sector needs to be smaller than the analogous in the sdown-squark sector in order to satisfy the bound imposed by the decay of {tau}{yields}{mu}{mu}.
Leptonic mixing, family symmetries, and neutrino phenomenology
Medeiros Varzielas, I. de; Gonzalez Felipe, R.; Serodio, H.
2011-02-01
Tribimaximal leptonic mixing is a mass-independent mixing scheme consistent with the present solar and atmospheric neutrino data. By conveniently decomposing the effective neutrino mass matrix associated to it, we derive generic predictions in terms of the parameters governing the neutrino masses. We extend this phenomenological analysis to other mass-independent mixing schemes which are related to the tribimaximal form by a unitary transformation. We classify models that produce tribimaximal leptonic mixing through the group structure of their family symmetries in order to point out that there is often a direct connection between the group structure and the phenomenological analysis. The type of seesaw mechanism responsible for neutrino masses plays a role here, as it restricts the choices of family representations and affects the viability of leptogenesis. We also present a recipe to generalize a given tribimaximal model to an associated model with a different mass-independent mixing scheme, which preserves the connection between the group structure and phenomenology as in the original model. This procedure is explicitly illustrated by constructing toy models with the transpose tribimaximal, bimaximal, golden ratio, and hexagonal leptonic mixing patterns.
Supersymmetric musings on the predictivity of family symmetries
Kadota, Kenji; Kersten, Joern; Velasco-Sevilla, Liliana
2010-10-15
We discuss the predictivity of family symmetries for the soft supersymmetry breaking parameters in the framework of supergravity. We show that unknown details of the messenger sector and the supersymmetry breaking hidden sector enter into the soft parameters, making it difficult to obtain robust predictions. We find that there are specific choices of messenger fields which can improve the predictivity for the soft parameters.
NASA Astrophysics Data System (ADS)
Sourrouille, Lucas
2015-11-01
We consider a generalization of non-relativistic Schrödinger-Higgs Lagrangian by introducing a nonstandard kinetic term. We show that this model is Galilean invariant, we construct the conserved charges associated to the symmetries and realize the algebra of the Galilean group. In addition, we study the model in the presence of a gauge field. We also show that the gauged model is Galilean invariant. Finally, we explore relations between the twin models and their solutions.
Majorana meets Coxeter: Non-Abelian Majorana fermions and non-Abelian statistics
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2011-04-01
We discuss statistics of vortices having zero-energy non-Abelian Majorana fermions inside them. Considering the system of multiple non-Abelian vortices, we derive a non-Abelian statistics that differs from the previously derived non-Abelian statistics. The non-Abelian statistics presented here is given by a tensor product of two different groups, namely the non-Abelian statistics obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter group is a symmetric group related to the symmetry of polytopes in a high-dimensional space. As the simplest example, we consider the case in which a vortex contains three Majorana fermions that are mixed with each other under the SO(3) transformations. We concretely present the representation of the Coxeter group in our case and its geometrical expressions in the high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.
Lepton mixing in A 5 family symmetry and generalized CP
NASA Astrophysics Data System (ADS)
Li, Cai-Chang; Ding, Gui-Jun
2015-05-01
We study lepton mixing patterns which can be derived from the A 5 family symmetry and generalized CP. We find five phenomenologically interesting mixing patterns for which one column of the PMNS matrix is (the first column of the golden ratio mixing), (the second column of the golden ratio mixing), or . The three lepton mixing angles are determined in terms of a single real parameter θ, and agreement with experimental data can be achieved for certain values of θ. The Dirac CP violating phase is predicted to be trivial or maximal while Majorana phases are trivial. We construct a supersymmetric model based on A 5 family symmetry and generalized CP. The lepton mixing is exactly the golden ratio pattern at leading order, and the mixing patterns of case III and case IV are reproduced after higher order corrections are considered.
Optical Abelian lattice gauge theories
Tagliacozzo, L.; Celi, A.; Zamora, A.; Lewenstein, M.
2013-03-15
We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4 Multiplication-Sign 4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper. - Highlights: Black-Right-Pointing-Pointer We study the quantum simulation of dynamical gauge theories in optical lattices. Black-Right-Pointing-Pointer We focus on digital simulation of abelian lattice gauge theory. Black-Right-Pointing-Pointer We rediscover and discuss the puzzling phase diagram of gauge magnets. Black-Right-Pointing-Pointer We detail the protocol for time evolution and ground-state preparation in any phase. Black-Right-Pointing-Pointer We provide two experimental tests to validate gauge theory quantum simulators.
DERMATOGLYPHIC FLUCTUATING ASYMMETRY AND SYMMETRY IN FAMILIAL AND NON FAMILIAL SCHIZOPHRENIA
Ponnudurai, R.; Menon, M. Sarada; Muthu, M.
1997-01-01
Three dermatoglyphic traits, viz; finger patterns, finger ridge counts, and palmer a-b ridge counts of 57 (M-29; F-28) and 64 (M-29; F-35). Schizophrenics with and without positive family history respectively, and 65 controls (M-30, F-35), were analysed to determine their level of fluctuating asymmetry. Uniformly higher fluctuating asymmetry was observed in the loop ridge counts of second digits of males and females of both the groups of schizophrenics. Significantly increased symmetry in the right and left loop ridge counts in the fifth digits of the family history positive female patients was noted. Barring the family history positive female schizophrenics, the rest of the patient groups manifested higher fluctuating asymmetry in their right and left whorl ridge counts of fourth digits. Family history positive patients of both sexes and female patients with negative family history displayed higher fluctuating asymmetry in the right and left palmer a-b ridge counts. PMID:21584076
Non-Abelian quasigapless modes localized on mass vortices in superfluid He3-B
NASA Astrophysics Data System (ADS)
Nitta, Muneto; Shifman, Mikhail; Vinci, Walter
2013-04-01
Kelvin waves, or Kelvons, have been known for a long time as gapless excitations propagating along superfluid vortices. These modes can be interpreted as the Nambu-Goldstone excitations arising from the spontaneous breaking of the translational symmetry. Recently a different type of gapless excitation localized on strings—the so-called non-Abelian mode—attracted much attention in high-energy physics. We discuss their relevance in condensed matter physics. Non-Abelian rotational quasigapless excitations could appear on the mass vortices in the B phase of the superfluid He3, due to the fact that the order parameter in He3-B is tensorial. While the U(1) rotational excitations are well established in vortices with asymmetric cores, the non-Abelian rotational excitations belonging to the same family were not considered.
Progressive gauge U(1) family symmetry for quarks and leptons
NASA Astrophysics Data System (ADS)
Ma, Ernest
2016-08-01
The pattern of quark and lepton mass matrices is unexplained in the standard model of particle interactions. I propose the novel idea of a progressive gauge U (1 ) symmetry where it is a reflection of the regressive electroweak symmetry breaking pattern, caused by an extended Higgs scalar sector. Phenomenological implications of this new hypothesis are discussed.
Köppl, Christoph; Werner, Hans-Joachim
2015-04-28
Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.
Lepton mixing parameters from Δ(48) family symmetry and generalised CP
NASA Astrophysics Data System (ADS)
Ding, Gui-Jun; Zhou, Ye-Ling
2014-06-01
We provide a systematic and thorough exploration of the Δ(48) family symmetry and the consistent generalised CP symmetry. A model-independent analysis of the achievable lepton flavor mixing is performed by considering all the possible remnant symmetries in the neutrino and the charged lepton sectors. We find a new interesting mixing pattern in which both lepton mixing angles and CP phases are nontrivial functions of a single parameter θ. The value of θ can be fixed by the measured reactor mixing angle θ 13, and the excellent agreement with the present data can be achieved. A supersymmetric model based on Δ(48) family symmetry and generalised CP symmetry is constructed, and this new mixing pattern is exactly reproduced.
Symmetries and color symmetries of a family of tilings with a singular point.
Evidente, Imogene F; Felix, Rene P; Loquias, Manuel Joseph C
2015-11-01
Tilings with a singular point are obtained by applying conformal maps on regular tilings of the Euclidean plane and their symmetries are determined. The resulting tilings are then symmetrically colored by applying the same conformal maps on colorings of regular tilings arising from sublattice colorings of the centers of the tiles. In addition, conditions are determined in order that the coloring of a tiling with singularity that is obtained in this manner is perfect. PMID:26522407
Generalised CP and trimaximal TM1 lepton mixing in S4 family symmetry
NASA Astrophysics Data System (ADS)
Li, Cai-Chang; Ding, Gui-Jun
2014-04-01
We construct two flavor models based on S4 family symmetry and generalised CP symmetry. In both models, the S4 family symmetry is broken down to the Z2SU subgroup in the neutrino sector, as a consequence, the trimaximal TM1 lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed. Nevertheless, the flavon fields enter into the Majorana mass terms at leading order in the second model. The leading order lepton mixing is of the tri-bimaximal form which is broken down to TM1 by the next to leading order contributions.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Neutrinos and flavor symmetries
NASA Astrophysics Data System (ADS)
Tanimoto, Morimitsu
2015-07-01
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Deviation from bimaximal mixing and leptonic CP phases in S 4 family symmetry and generalized CP
NASA Astrophysics Data System (ADS)
Li, Cai-Chang; Ding, Gui-Jun
2015-08-01
The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a mixing matrix from S 4 family symmetry and generalized CP symmetry H CP. Supposing that S 4 ⋊ H CP is broken down to in the neutrino sector and in the charged lepton sector, one column of the PMNS matrix would be of the form up to permutations, both Dirac CP phase and Majorana CP phases are trivial to accommodate the observed lepton mixing angles. The phenomenological implications of the remnant symmetry in the neutrino sector and Z {2/ SU } × H {CP/ l } in the charged lepton sector are studied. One row of PMNS matrix is determined to be , and all the three leptonic CP phases can only be trivial to fit the measured values of the mixing angles. Two models based on S 4 family symmetry and generalized CP are constructed to implement these model independent predictions enforced by remnant symmetry. The correct mass hierarchy among the charged leptons is achieved. The vacuum alignment and higher order corrections are discussed.
Infrared Maximally Abelian Gauge
Mendes, Tereza; Cucchieri, Attilio; Mihara, Antonio
2007-02-27
The confinement scenario in Maximally Abelian gauge (MAG) is based on the concepts of Abelian dominance and of dual superconductivity. Recently, several groups pointed out the possible existence in MAG of ghost and gluon condensates with mass dimension 2, which in turn should influence the infrared behavior of ghost and gluon propagators. We present preliminary results for the first lattice numerical study of the ghost propagator and of ghost condensation for pure SU(2) theory in the MAG.
On spectroscopy for a whole Abelian model
Chauca, J.; Doria, R.
2012-09-24
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 {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.
Bell diagonal states with maximal Abelian symmetry
Chruscinski, Dariusz; Kossakowski, Andrzej
2010-12-15
We provide a simple class of 2-qudit states for which one is able to formulate necessary and sufficient conditions for separability. As a by-product, we generalize the well-known construction provided by Horodecki et al. [Phys. Rev. Lett. 82, 1056 (1999)] for d=3. It is hoped that these states with known separability and entanglement properties may be used to test various notions in entanglement theory.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Gravitating non-Abelian cosmic strings
NASA Astrophysics Data System (ADS)
de Pádua Santos, Antônio; Bezerra de Mello, Eugênio R.
2015-08-01
In this paper, we study regular cosmic string solutions of the non-Abelian Higgs model coupled with gravity. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically. The solutions we are interested in asymptote to a flat spacetime with a planar angle deficit. The model under consideration presents two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling, so we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as a function of the energy scale where the gauge symmetry is spontaneously broken.
SU (3)F gauge family model and new symmetry breaking scale from FCNC processes
NASA Astrophysics Data System (ADS)
Bao, Shou-Shan; Liu, Zhuo; Wu, Yue-Liang
2016-03-01
Based on the SU (3)F gauge family symmetry model which was proposed to explain the observed mass and mixing pattern of neutrinos, we investigate the symmetry breaking, the mixing pattern in quark and lepton sectors, and the contribution of the new gauge bosons to some flavour changing neutral currents (FCNC) processes at low energy. With the current data of the mass differences in the neutral pseudo-scalar P0-Pbar0 systems, we find that the SU (3)F symmetry breaking scale can be as low as 300 TeV and the mass of the lightest gauge boson be about 100 TeV. Other FCNC processes, such as the lepton flavour number violation process μ- →e-e+e- and the semi-leptonic rare decay K → π ν bar ν, contain contributions via the new gauge bosons exchanging. With the constrains obtained from P0-Pbar0 system, we estimate that the contribution of the new physics is around 10-16, far below the current experimental bounds.
Flavor symmetry based MSSM: Theoretical models and phenomenological analysis
NASA Astrophysics Data System (ADS)
Babu, K. S.; Gogoladze, Ilia; Raza, Shabbar; Shafi, Qaisar
2014-09-01
We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM—for flavor symmetry-based minimal supersymmetric standard model—that respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)H and SO(3)H with the three families transforming as 2+1 and 3 representations, respectively. A simple solution is found in the case of SU(2)H for suppressing the flavor violating D-terms based on an exchange symmetry. Explicit models based on SO(3)H without the D-term problem are developed. In addition, models based on discrete non-Abelian flavor groups are presented which are automatically free from D-term issues. The permutation group S3 with a 2+1 family assignment, as well as the tetrahedral group A4 with a 3 assignment are studied. In all cases, a simple solution to the SUSY CP problem is found, based on spontaneous CP violation leading to a complex quark mixing matrix. We develop the phenomenology of the resulting sMSSM, which is controlled by seven soft SUSY breaking parameters for both the 2+1 assignment and the 3 assignment of fermion families. These models are special cases of the phenomenological MSSM (pMSSM), but with symmetry restrictions. We discuss the parameter space of sMSSM compatible with LHC searches, B-physics constraints and dark matter relic abundance. Fine-tuning in these models is relatively mild, since all SUSY particles can have masses below about 3 TeV.
A Model of Fermion Masses and Flavor Mixings with Family Symmetry SU(3) otimes U(1)
NASA Astrophysics Data System (ADS)
Yang, Wei-Min; Wang, Qi; Zhong, Jin-Jin
2012-01-01
The family symmetry SU(3) otimes U(1) is proposed to solve flavor problems about fermion masses and flavor mixings. It is breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z2 is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of θl13 and JlCP in neutrino physics. All of the results are promising to be tested in the future experiments.
Non-Abelian Meissner effect in Yang-Mills theories at weak coupling
Gorsky, A.; Shifman, M.; Yung, A.
2005-02-15
We present a weak-coupling Yang-Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles we get gluelumps which convert a 'QCD string' in the excited state to that in the ground state. Introducing a mass parameter m we discover a phase transition between the Abelian and non-Abelian confinement at a critical value m=m{sub *}{approx}{lambda}. Underlying dynamics are governed by a Z{sub N} symmetry inherent to the model under consideration. At m>m{sub *} the Z{sub N} symmetry is spontaneously broken, resulting in N degenerate Z{sub N} (Abelian) strings. At m
On whole Abelian model dynamics
Chauca, J.; Doria, R.
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 oriented 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.
Non-Abelian vortices with a twist
NASA Astrophysics Data System (ADS)
Forgács, Péter; Lukács, Árpád; Schaposnik, Fidel A.
2015-06-01
Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of four-dimensional N =2 supersymmetric gauge theories. The specific model considered here possesses U(2 ) local×SU(2 ) global symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary and translationally symmetric along the x3 direction, and they are characterized by a matrix phase between the two doublets, referred to as "twist." Consequently, twisted strings have nonzero (global) charge, momentum, and in some cases even angular momentum per unit length. The planar cross section of a twisted string corresponds to a rotationally symmetric, charged non-Abelian vortex, satisfying first-order Bogomolny-type equations and second-order Gauss constraints. Interestingly, depending on the nature of the matrix phase, some of these solutions even break cylindrical symmetry in R3. Although twisted vortices have higher energy than the untwisted ones, they are expected to be linearly stable since one can keep their charge (or twist) fixed with respect to small perturbations.
Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory
NASA Astrophysics Data System (ADS)
Kumar, R.; Krishna, S.; Shukla, A.; Malik, R. P.
2014-09-01
Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space-time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space-time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space-time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.
Abelian and non-Abelian Hopfions in all odd dimensions
NASA Astrophysics Data System (ADS)
Radu, Eugen; Tchrakian, Tigran
2014-10-01
We extend the definition of the topological charge pertaining to the CP1 (i.e. O(3)) Skyrme-Fadde'ev Hopfion on Bbb R3 to candidates for topological charges of Bbb CPn sigma models on Bbb R2n+1 for all n. For this, the Abelian composite connections of the Bbb CPn sigma models are employed. In higher dimensions (n >= 1) it turns out that such charges, described by the nonAbelian composite connections of suitable Grassmannian sigma models, can also be constructed. A concrete discussion of the non-Abelian case for n = 2 is presented.
Symmetries of Mücket-Treder's two-body problem
NASA Astrophysics Data System (ADS)
Mioc, V.
The two-body problem associated to the classical potential field proposed by Mücket and Treder (1977) is considered from the only standpoint of symmetries. The corresponding vector field in Hamiltonian or standard polar coordinates presents nice symmetries that form eight-element symmetric Abelian groups endowed with an idempotent structure. Expressed in Levi-Civita coordinates, the problem exhibits a sixteen-element group of symmetries, also Abelian and presenting an idempotent structure.
Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family
Das, Tanmoy; Zhu, Jian-Xin; Graf, Matthias J.
2015-01-01
The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s+− wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s+− wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry. PMID:25721375
Theory of nodal s^{±}-wave pairing symmetry in the Pu-based 115 superconductor family
Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.
2015-02-27
The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-T_{c} superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel, which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.
Theory of nodal s±-wave pairing symmetry in the Pu-based 115 superconductor family
Das, Tanmoy; Zhu, Jian -Xin; Graf, Matthias J.
2015-02-27
The spin-fluctuation mechanism of superconductivity usually results in the presence of gapless or nodal quasiparticle states in the excitation spectrum. Nodal quasiparticle states are well established in copper-oxide, and heavy-fermion superconductors, but not in iron-based superconductors. Here, we study the pairing symmetry and mechanism of a new class of plutonium-based high-Tc superconductors and predict the presence of a nodal s⁺⁻ wave pairing symmetry in this family. Starting from a density-functional theory (DFT) based electronic structure calculation we predict several three-dimensional (3D) Fermi surfaces in this 115 superconductor family. We identify the dominant Fermi surface “hot-spots” in the inter-band scattering channel,more » which are aligned along the wavevector Q = (π, π, π), where degeneracy could induce sign-reversal of the pairing symmetry. Our calculation demonstrates that the s⁺⁻ wave pairing strength is stronger than the previously thought d-wave pairing; and more importantly, this pairing state allows for the existence of nodal quasiparticles. Finally, we predict the shape of the momentum- and energy-dependent magnetic resonance spectrum for the identification of this pairing symmetry.« less
Origin of families and S O (18 ) grand unification
NASA Astrophysics Data System (ADS)
BenTov, Yoni; Zee, A.
2016-03-01
We exploit a recent advance in the study of interacting topological superconductors to propose a solution to the family puzzle of particle physics in the context of S O (18 ) [or more correctly, Spin(18 )] grand unification. We argue that Yukawa couplings of intermediate strength may allow the mirror matter and extra families to decouple at arbitrarily high energies. As was clear from the existing literature, we have to go beyond the Higgs mechanism in order to solve the family puzzle. A pattern of symmetry breaking which results in the S U (5 ) grand unified theory with horizontal or family symmetry U S p (4 )=Spin(5 ) [or more loosely, S O (5 )] leaves exactly three light families of matter and seems particularly appealing. We comment briefly on an alternative scheme involving discrete non-Abelian family symmetries. In a few lengthy Appendices we review some of the pertinent condensed matter theory.
Search for electron liquids with non-Abelian quasiparticles
NASA Astrophysics Data System (ADS)
Wójs, Arkadiusz
2010-03-01
We use exact numerical diagonalization in the search of fractional quantum Hall states with non-Abelian quasiparticle statistics. For the (most promising) states in a partially filled second Landau level, the search is narrowed to the range of filling factors 7/3 < ve < 8/3. In this range, the analysis of energy spectra and correlation functions, calculated including finite width and Landau level mixing, supports the prominent non-Abelian candidates at ve = 5/2 (paired Moore-Read "pfafian" state) and 12/5 (clustered Read-Rezayi "parafermion" state). Outside of this range, the noninteracting composite fermion model with four attached flux quanta is validated, yielding the family of quantum liquids with fractional, but Abelian statistics. The borderline ve = 7/3 state is shown to be adiabatically connected to the Laughlin liquid, but its short-range correlations are significantly different.
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Two-component Abelian sandpile models.
Alcaraz, F C; Pyatov, P; Rittenberg, V
2009-04-01
In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches. PMID:19518280
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…
Inversion symmetry breaking by oxygen octahedral rotations in the Ruddlesden-Popper NaRTiO4 family.
Akamatsu, Hirofumi; Fujita, Koji; Kuge, Toshihiro; Sen Gupta, Arnab; Togo, Atsushi; Lei, Shiming; Xue, Fei; Stone, Greg; Rondinelli, James M; Chen, Long-Qing; Tanaka, Isao; Gopalan, Venkatraman; Tanaka, Katsuhisa
2014-05-01
Rotations of oxygen octahedra are ubiquitous, but they cannot break inversion symmetry in simple perovskites. However, in a layered oxide structure, this is possible, as we demonstrate here in A-site ordered Ruddlesden-Popper NaRTiO4 (R denotes rare-earth metal), previously believed to be centric. By revisiting this series via synchrotron x-ray diffraction, optical second-harmonic generation, piezoresponse force microscopy, and first-principles phonon calculations, we find that the low-temperature phase belongs to the acentric space group P42(1)m, which is piezoelectric and nonpolar. The mechanism underlying this large new family of acentric layered oxides is prevalent, and could lead to many more families of acentric oxides.
On the quantum corrections to two-dimensional (1,0)-supersymmetric Abelian gauge models
Almeida, C.A.S.; De Oliveira, M.W. ); Kneipp, M.A.C. )
1991-05-30
In this paper the machinery of (1,0)-supergravity is employed to evaluate 1-loop corrections to the effective action and chiral symmetry supercurrent in the framework of an (1,0)-supersymmetric Abelian gauge model. As a by-product, a dynamically-generated mass is found out for the gauge (1,0)-superconductions.
Globally symmetric topological phase: from anyonic symmetry to twist defect.
Teo, Jeffrey C Y
2016-04-13
Topological phases in two dimensions support anyonic quasiparticle excitations that obey neither bosonic nor fermionic statistics. These anyon structures often carry global symmetries that relate distinct anyons with similar fusion and statistical properties. Anyonic symmetries associate topological defects or fluxes in topological phases. As the symmetries are global and static, these extrinsic defects are semiclassical objects that behave disparately from conventional quantum anyons. Remarkably, even when the topological states supporting them are Abelian, they are generically non-Abelian and powerful enough for topological quantum computation. In this article, I review the most recent theoretical developments on symmetries and defects in topological phases.
Twist Defects in Topological Systems with Anyonic Symmetries
NASA Astrophysics Data System (ADS)
Teo, Jeffrey; Roy, Abhishek; Chen, Xiao
2014-03-01
Twist defects are point-like objects that support robust non-local storage of quantum information and non-abelian unitary operations. Unlike quantum deconfined anyonic excitations, they rely on symmetry rather than a non-abelian topological order. Zero energy Majorana bound states can arise at lattice defects, such as disclinations and dislocations, in a topological crystalline superconductor. More general parafermion bound state can appear as twist defects in a topological phase with an anyonic symmetry, such as a bilayer fractional quantum Hall state and the Kitaev toric code. They are however fundamentally different from quantum anyonic excitations in a true topological phase. This is demonstrated by their unconventional exchange and braiding behavior, which is characterized by a modified spin statistics theorem and modular invariance. Gauging anyonic symmetries by treating twist defects as quantum excitations provides a connection between some non-abelian topological states and abelian ones. Simons Foundation
Ermakov's Superintegrable Toy and Nonlocal Symmetries
NASA Astrophysics Data System (ADS)
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Abelian cosmic string in the Starobinsky model of gravity
NASA Astrophysics Data System (ADS)
Morais Graça, J. P.
2016-03-01
In this paper, I analyze numerically the behaviour of the solutions corresponding to an Abelian string in the framework of the Starobinsky model. The role played by the quadratic term in the Lagrangian density f(R)=R+η {R}2 of this model is emphasized and the results are compared with the corresponding ones obtained in the framework of Einstein’s theory of gravity. I have found that the angular deficit generated by the string is lowered as the η parameter increases, allowing a well-behaved spacetime for a large range of values of the symmetry-breaking scale.
Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
NASA Astrophysics Data System (ADS)
Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.
2016-04-01
To explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine-tuning of prefactors. Fitting with quark and lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic C P violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.
Unification of gauge, family, and flavor symmetries illustrated in gauged SU(12) models
Albright, Carl H.; Feger, Robert P.; Kephart, Thomas W.
2016-04-25
In this study, to explain quark and lepton masses and mixing angles, one has to extend the standard model, and the usual practice is to put the quarks and leptons into irreducible representations of discrete groups. We argue that discrete flavor symmetries (and their concomitant problems) can be avoided if we extend the gauge group. In the framework of SU(12) we give explicit examples of models having varying degrees of predictability obtained by scanning over groups and representations and identifying cases with operators contributing to mass and mixing matrices that need little fine- tuning of prefactors. Fitting with quark andmore » lepton masses run to the GUT scale and known mixing angles allows us to make predictions for the neutrino masses and hierarchy, the octant of the atmospheric mixing angle, leptonic CP violation, Majorana phases, and the effective mass observed in neutrinoless double beta decay.« less
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.
Mixed symmetry tensors in the worldline formalism
NASA Astrophysics Data System (ADS)
Corradini, Olindo; Edwards, James P.
2016-05-01
We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U( F ) "flavour" symmetry on the world-line particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.
Vortex states in a non-Abelian magnetic field
NASA Astrophysics Data System (ADS)
Nikolić, Predrag
2016-08-01
A type-II superconductor survives in an external magnetic field by admitting an Abrikosov lattice of quantized vortices. This is an imprint of the Aharonov-Bohm effect created by the Abelian U(1) gauge field. The simplest non-Abelian analog of such a gauge field, which belongs to the SU(2) symmetry group, can be found in topological insulators. Here we discover a superconducting ground state with a lattice of SU(2) vortices in a simple two-dimensional model that presents an SU(2) "magnetic" field (invariant under time reversal) to attractively interacting fermions. The model directly captures the correlated topological insulator quantum well, and approximates one channel for instabilities on the Kondo topological insulator surface. Due to its simplicity, the model might become amenable to cold atom simulations in the foreseeable future. The vitality of low-energy vortex states born out of SU(2) magnetic fields is promising for the creation of incompressible vortex liquids with non-Abelian fractional excitations.
Abelian duality at higher genus
NASA Astrophysics Data System (ADS)
Beasley, Chris
2014-07-01
In three dimensions, a free, periodic scalar field is related by duality to an abelian gauge field. Here I explore aspects of this duality when both theories are quantized on a Riemann surface of genus g. At higher genus, duality involves an identification of winding with momentum on the Jacobian variety of the Riemann surface. I also consider duality for monopole and loop operators on the surface and exhibit the operator algebra, a refinement of the Wilson-'t Hooft algebra.
Surface defects and symmetries
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph
2015-04-01
In quantum field theory, defects of various codimensions are natural ingredients and carry a lot of interesting information. In this contribution we concentrate on topological quantum field theories in three dimensions, with a particular focus on Dijkgraaf-Witten theories with abelian gauge group. Surface defects in Dijkgraaf-Witten theories have applications in solid state physics, topological quantum computing and conformal field theory. We explain that symmetries in these topological field theories are naturally defined in terms of invertible topological surface defects and are thus Brauer-Picard groups.
Family nonuniversal U(1){sup '} gauge symmetries and b{yields}s transitions
Barger, Vernon; Everett, Lisa; Jiang Jing; Langacker, Paul; Liu Tao; Wagner, Carlos E. M.
2009-09-01
We present a correlated analysis for the {delta}B=1, 2 processes which occur via b{yields}s transitions within models with a family nonuniversal U(1){sup '}. We take a model-independent approach and only require family universal charges for the first and second generations and small fermion mixing angles. The results of our analysis show that within this class of models, the anomalies in B{sub s}-B{sub s} mixing and the time-dependent CP asymmetries of the penguin-dominated B{sub d}{yields}({pi},{phi},{eta}{sup '},{rho},{omega},f{sub 0})K{sub S} decays can be accommodated.
Family non-universal U(1)' gauge symmetries and b {r_arrow} s transitions.
Barger, V.; Everett, L.; Jiang, J.; Langacker, P.; Liu, T.; Wagner, C .E. M.; High Energy Physics; Univ. of Chicago; Univ. of Wisconsin at Madison; Inst. for Advanced Study
2009-01-01
We present a correlated analysis for the {Delta}B = 1, 2 processes which occur via b {yields} s transitions within models with a family nonuniversal U(1){prime}. We take a model-independent approach and only require family universal charges for the first and second generations and small fermion mixing angles. The results of our analysis show that within this class of models, the anomalies in B{sub s}-B{sub s}{sup -} mixing and the time-dependent CP asymmetries of the penguin-dominated B{sub d} {yields} ({pi},{psi},{eta}{prime},{rho},{omega},f{sub 0})K{sub S} decays can be accommodated.
Abelian-Higgs strings in Rastall gravity
NASA Astrophysics Data System (ADS)
Bezerra de Mello, Eugênio R.; Fabris, Júlio C.; Hartmann, Betti
2015-04-01
In this paper we analyze Abelian-Higgs strings in a phenomenological model that takes quantum effects in curved space-time into account. This model, first introduced by Rastall, cannot be derived from an action principle. We formulate phenomenological equations of motion under the guiding principle of minimal possible deformation of the standard equations. We construct string solutions that asymptote to a flat space-time with a deficit angle by solving the set of coupled nonlinear ordinary differential equations numerically. Decreasing the Rastall parameter from its Einstein gravity value, we find that the deficit angle of the space-time increases and becomes equal to 2π at some critical value of this parameter that depends on the remaining couplings in the model. For smaller values, the resulting solutions are supermassive string solutions possessing a singularity at a finite distance from the string core. Assuming the Higgs boson mass to be on the order of the gauge boson mass, we also find that in Rastall gravity this happens only when the symmetry breaking scale is on the order of the Planck mass. We observe that for specific values of the parameters in the model, the energy per unit length becomes proportional to the winding number, i.e. the degree of the map {{S}1}\\to {{S}1}. Unlike in the Bogomolnyi-Prasad-Sommerfield (BPS) limit in Einstein gravity, this is, however, not connected to an underlying mathematical structure, but rather constitutes a would-be-BPS bound.
Symmetries and vanishing couplings in string-derived low energy effective field theory
Kobayashi, Tatsuo
2012-07-27
We study 4D low-energy effective field theory, derived from heterotic string theory on the orbifolds. In particular, we study Abelian and non-Abelian discrete symmetries and their anomalies. Furthermore, stringy computations also provide with stringy coupling selection rules.
Models for neutrino mass with discrete symmetries
NASA Astrophysics Data System (ADS)
Morisi, S.
2011-08-01
Discrete non-abelian flavor symmetries give in a natural way tri-bimaximal (TBM) mixing as showed in a prototype model. However neutrino mass matrix pattern may be very different from the tri-bimaximal one if small deviations of TBM will be observed. We give the result of a model independent analysis for TBM neutrino mass pattern.
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
NASA Astrophysics Data System (ADS)
Pinho, Suani T. R.; Andrade, Roberto F. S.
Statistical analyses of long-term records of daily rain suggest that rain phenomena might be a manifestation of self-organized criticality. In this work the essential mechanisms of rain phenomena, the growth of droplets inside a cloud and the subsequent rainfall, are described by an Abelian sandpile model of self-organized criticality. Several simulations support the existence of scale invariance. The introduction of variations of the basic model, to provide a better description of the phenomena, does not alter the critical behavior.
Monopoles, Abelian projection, and gauge invariance
Bonati, Claudio; Di Giacomo, Adriano; Lepori, Luca; Pucci, Fabrizio
2010-04-15
A direct connection is proved between the non-Abelian Bianchi Identities (NABI's) and the Abelian Bianchi identities for the 't Hooft tensor. As a consequence, the existence of a nonzero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows us to show that not all Abelian projections can be used to expose monopoles in lattice configurations: each field configuration with nonzero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-Abelian gauge is a legitimate choice. It is also proven, starting from the NABI, that monopole condensation is a physical gauge-invariant phenomenon, independent of the choice of the Abelian projection.
NASA Astrophysics Data System (ADS)
Ortín, Tomás; Ramírez, Pedro F.
2016-09-01
We construct a supersymmetric black ring solution of SU (2) N = 1, d = 5 Super-Einstein-Yang-Mills (SEYM) theory by adding a distorted BPST instanton to an Abelian black ring solution of the same theory. The change cannot be observed from spatial infinity: neither the mass, nor the angular momenta or the values of the scalars at infinity differ from those of the Abelian ring. The entropy is, however, sensitive to the presence of the non-Abelian instanton, and it is smaller than that of the Abelian ring, in analogy to what happens in the supersymmetric colored black holes recently constructed in the same theory and in N = 2, d = 4 SEYM. By taking the limit in which the two angular momenta become equal we derive a non-Abelian generalization of the BMPV rotating black-hole solution.
NASA Astrophysics Data System (ADS)
Barker, J. A. T.; Singh, D.; Thamizhavel, A.; Hillier, A. D.; Lees, M. R.; Balakrishnan, G.; Paul, D. McK.; Singh, R. P.
2015-12-01
The superconductivity of the noncentrosymmetric compound La7 Ir3 is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature Tc=2.25 K —a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La7 Ir3 may be unconventional and paves the way for further studies of this family of materials.
A 3-3-1 model with right-handed neutrinos based on the Δ ( 27) family symmetry
NASA Astrophysics Data System (ADS)
Hernández, A. E. Cárcamo; Long, H. N.; Vien, V. V.
2016-05-01
We present the first multiscalar singlet extension of the original 3-3-1 model with right-handed neutrinos, based on the Δ ( 27) family symmetry, supplemented by the Z4⊗ Z8⊗ Z_{14} flavor group, consistent with current low energy fermion flavor data. In the model under consideration, the light active neutrino masses are generated from a double seesaw mechanism and the observed pattern of charged fermion masses and quark mixing angles is caused by the breaking of the Δ ( 27) ⊗ Z4⊗ Z8⊗ Z_{14} discrete group at very high energy. Our model has only 14 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for the quark sector agree with their experimental values, whereas those for the lepton sector also do, only for the inverted neutrino mass hierarchy. The normal neutrino mass hierarchy scenario of the model is disfavored by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of m_{β β }= 22 meV, a leptonic Dirac CP violating phase of 34°, and a Jarlskog invariant of about 10^{-2} for the inverted neutrino mass spectrum.
NMR, symmetry elements, structure and phase transitions in the argyrodite family
NASA Astrophysics Data System (ADS)
Gaudin, E.; Taulelle, F.; Boucher, F.; Evain, M.
1998-02-01
Cu7PSe6 belongs to a family of structures known as the argyrodites. It undergoes two phases transitions. The high temperature phase has been determined by X-ray diffraction. It has a Foverline{4}3m space group. Medium temperature phases have been refined using a non-harmonic technique and the space group proposed is P213. The low temperature phase had an apparent space group of Foverline{4}3m also. Use of X-ray diffraction and NMR together has allowed to determine the space groups of all phases as being respectively Foverline{4}3m, P213 and Pmn21. Positioning of disordered coppers in the structure is therefore possible and the structure can be described by connex polyhedra of PSe3-4 and SeCux-2_x. The phase transitions can be understood by an ordered motion of SeCux-2x polyhedra. If these polyhedra set in motion independently two transitions are to be observed, if they are coupled only one is observed. Cu7PSe6 appartient à une famille de composés connus sous le nom d'argyrodites. Cu7PSe6 possède deux transitions de phase. La structure de haute température a été déterminée par diffraction des rayons X. Elle se décrit par le groupe d'espace Foverline{4}3m. La phase de moyenne température a été raffinée en utilisant une technique non-harmonique et le groupe d'espace proposé est P213. La phase de basse température possède également un groupe d'espace apparent Foverline{4}3m. En utilisant ensemble la diffraction des rayons X et la RMN, il a été possible de déterminer les groupes d'espace de toutes les phases comme étant respectivement Foverline{4}3m, P213 et Pmn21. Placer les atomes de cuivre, désordonnés, dans la structure devient alors possible et la structure peut se décrire comme un ensemble de polyèdres connexes de PSe3-4 et SeCux-2_x. Les transitions de phases se décrivent alors comme des mouvements ordonnés des polyèdres SeCux-2_x. Si ces polyèdres se mettent en mouvement indépendamment, deux transitions de phases sont attendues, si
Adler, S.L.
1999-01-01
We construct extensions of the standard model based on the hypothesis that Higgs bosons also exhibit a family structure and that the flavor weak eigenstates in the three families are distinguished by a discrete Z{sub 6} chiral symmetry that is spontaneously broken by the Higgs sector. We study in detail at the tree level models with three Higgs doublets and with six Higgs doublets comprising two weakly coupled sets of three. In a leading approximation of S{sub 3} cyclic permutation symmetry the three-Higgs-doublet model gives a {open_quotes}democratic{close_quotes} mass matrix of rank 1, while the six-Higgs-doublet model gives either a rank-1 mass matrix or, in the case when it spontaneously violates {ital CP}, a rank-2 mass matrix corresponding to nonzero second family masses. In both models, the CKM matrix is exactly unity in the leading approximation. Allowing small explicit violations of cyclic permutation symmetry generates small first family masses in the six-Higgs-doublet model, and first and second family masses in the three-Higgs-doublet model, and gives a nontrivial CKM matrix in which the mixings of the first and second family quarks are naturally larger than mixings involving the third family. Complete numerical fits are given for both models, flavor-changing neutral current constraints are discussed in detail, and the issues of unification of couplings and neutrino masses are addressed. On a technical level, our analysis uses the theory of circulant and retrocirculant matrices, the relevant parts of which are reviewed. {copyright} {ital 1998} {ital The American Physical Society}
Supersymmetry and non-Abelian T-duality in type II supergravity
NASA Astrophysics Data System (ADS)
Kelekci, Özgür; Lozano, Yolanda; Macpherson, Niall T.; Colgáin, Eoin Ó.
2015-02-01
We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the supersymmetry variations after T-duality are related to the variations before T-duality through the Kosmann spinorial Lie derivative, which vanishes when the Killing spinors are independent of the T-duality directions. As a byproduct of our analysis, we present closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a novel AdS3 geometry with large N=(4,4) superconformal symmetry.
NASA Astrophysics Data System (ADS)
Gerbier, Fabrice; Goldman, Nathan; Lewenstein, Maciej; Sengstock, Klaus
2013-07-01
Building a universal quantum computer is a central goal of emerging quantum technologies, which has the potential to revolutionize science and technology. Unfortunately, this future does not seem to be very close at hand. However, quantum computers built for a special purpose, i.e. quantum simulators , are currently developed in many leading laboratories. Many schemes for quantum simulation have been proposed and realized using, e.g., ultracold atoms in optical lattices, ultracold trapped ions, atoms in arrays of cavities, atoms/ions in arrays of traps, quantum dots, photonic networks, or superconducting circuits. The progress in experimental implementations is more than spectacular. Particularly interesting are those systems that simulate quantum matter evolving in the presence of gauge fields. In the quantum simulation framework, the generated (synthetic) gauge fields may be Abelian, in which case they are the direct analogues of the vector potentials commonly associated with magnetic fields. In condensed matter physics, strong magnetic fields lead to a plethora of fascinating phenomena, among which the most paradigmatic is perhaps the quantum Hall effect. The standard Hall effect consists in the appearance of a transverse current, when a longitudinal voltage difference is applied to a conducting sample. For quasi-two-dimensional semiconductors at low temperatures placed in very strong magnetic fields, the transverse conductivity, the ratio between the transverse current and the applied voltage, exhibits perfect and robust quantization, independent for instance of the material or of its geometry. Such an integer quantum Hall effect, is now understood as a deep consequence of underlying topological order. Although such a system is an insulator in the bulk, it supports topologically robust edge excitations which carry the Hall current. The robustness of these chiral excitations against backscattering explains the universality of the quantum Hall effect. Another
Symmetries of Fock's Two-Body Probmlem (II)
NASA Astrophysics Data System (ADS)
Mioc, Vasile; Rusu, Mircea; Stavinschi, Magda
A general view on the symmetries that characterize the two-body problem associated to Fock's field is provided. In both Cartesian or standard polar coordiantes, as well as in collision-blow-up and infinity-blow-up McGehee-type coordinates, these symmetries form isomorphic eight-element Abelian groups endowed with an idempotent structure. For Levi-Civita's regularizing coordinates, we find a sixteen-element group of symmetries with the same characteristics.
Abelian and non-Abelian bosonization: The operator solution of the WZW. sigma. model
do Amaral, R.L.P.G. ); Stephany Ruiz, J.E. )
1991-03-15
The complete equivalence between the Abelian and the non-Abelian bosonization formalisms for the treatment of SU({ital N}) fermions in two dimensions is analyzed and the operator solution of the Wess-Zumino-Witten nonlinear {sigma} model, written in terms of the scalar fields of the non-Abelian construction, is obtained. The importance of the order and disorder operators is stressed. In particular, they are used to show that an adequate reinterpretation of Mandelstam's formula gives the fermion representation in the non-Abelian bosonization formalism.
Conformal field theory approach to Abelian and non-Abelian quantum Hall quasielectrons.
Hansson, T H; Hermanns, M; Regnault, N; Viefers, S
2009-04-24
The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.
Local discrete symmetries from superstring derived models
NASA Astrophysics Data System (ADS)
Faraggi, Alon E.
1997-02-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Trapped fermions in a synthetic non-Abelian gauge field
Ghosh, Sudeep Kumar; Vyasanakere, Jayantha P.; Shenoy, Vijay B.
2011-11-15
On increasing the coupling strength ({lambda}) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density {rho}{approx}k{sub F}{sup 3} undergoes a change at a critical value, {lambda}{sub T}{approx_equal}k{sub F}[Phys. Rev. B 84, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-(1/2) fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing {lambda}. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling {lambda}. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Barker, J A T; Singh, D; Thamizhavel, A; Hillier, A D; Lees, M R; Balakrishnan, G; Paul, D McK; Singh, R P
2015-12-31
The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25 K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials. PMID:26765016
Barker, J A T; Singh, D; Thamizhavel, A; Hillier, A D; Lees, M R; Balakrishnan, G; Paul, D McK; Singh, R P
2015-12-31
The superconductivity of the noncentrosymmetric compound La(7)Ir(3) is investigated using muon spin rotation and relaxation. Zero-field measurements reveal the presence of spontaneous static or quasistatic magnetic fields below the superconducting transition temperature T(c)=2.25 K-a clear indication that the superconducting state breaks time-reversal symmetry. Furthermore, transverse-field rotation measurements suggest that the superconducting gap is isotropic and that the pairing symmetry of the superconducting electrons is predominantly s wave with an enhanced binding strength. The results indicate that the superconductivity in La(7)Ir(3) may be unconventional and paves the way for further studies of this family of materials.
ERIC Educational Resources Information Center
Forsythe, Susan K.
2015-01-01
This article describes a project using Design Based Research methodology to ascertain whether a pedagogical task based on a dynamic figure designed in a Dynamic Geometry Software (DGS) program could be instrumental in developing students' geometrical reasoning. A dragging strategy which I have named "Dragging Maintaining Symmetry" (DMS)…
Non-Abelian Braiding of Light.
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-12
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light. PMID:27563965
NASA Astrophysics Data System (ADS)
Iadecola, Thomas; Schuster, Thomas; Chamon, Claudio
2016-08-01
Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. In this work, we demonstrate that non-Abelian Berry phases can arise when coherent states of light are injected into "topological guided modes" in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell's equations, without resorting to the quantization of light. We propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.
Non-Abelian topological spin liquids from arrays of quantum wires or spin chains
NASA Astrophysics Data System (ADS)
Huang, Po-Hao; Chen, Jyong-Hao; Gomes, Pedro R. S.; Neupert, Titus; Chamon, Claudio; Mudry, Christopher
2016-05-01
We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in (1 +1 ) -dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges c <1 . These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.
Non-Abelian strings in high-density QCD: Zero modes and interactions
Nakano, Eiji; Nitta, Muneto; Matsuura, Taeko
2008-08-15
The most fundamental strings in high-density color superconductivity are the non-Abelian semisuperfluid strings which have color-gauge flux tubes but behave as superfluid vortices in the energetic point of view. We show that in addition to the usual translational zero modes, these vortices have normalizable orientational zero modes in the internal space, associated with the color-flavor locking symmetry broken in the presence of the strings. The interaction among two parallel non-Abelian semisuperfluid strings is derived for general relative orientational zero modes to show the universal repulsion. This implies that the previously known superfluid vortices, formed by spontaneously broken U(1){sub B}, are unstable to decay. Moreover, our result proves the stability of color superconductors in the presence of external color-gauge fields.
NASA Astrophysics Data System (ADS)
Yang, Fan; Liu, Ren-Bao
2014-12-01
We propose a general framework of nonlinear optics induced by non-Abelian Berry curvature in time-reversal-invariant (TRI) insulators. We find that the third-order response of a TRI insulator under optical and terahertz light fields is directly related to the integration of the non-Abelian Berry curvature over the Brillouin zone. We apply the result to insulators with rotational symmetry near the band edge. Under resonant excitations, the optical susceptibility is proportional to the flux of the Berry curvature through the iso-energy surface, which is equal to the Chern number of the surface times 2 π . For the III-V compound semiconductors, microscopic calculations based on the six-band model give a third-order susceptibility with the Chern number of the iso-energy surface equal to 3.
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
Neutrinos Masses in a Multi-Higgs Model with A4 symmetry
NASA Astrophysics Data System (ADS)
Machado, A. C. B.; Montero, J. C.; Pleitez, V.
2012-08-01
Presently it is well known that neutrino oscillation data are well described by massive neutrinos and their mixing. This suggests changes in the standard model (SM) and makes the flavor physics even more interesting. Recently, it has been proposed a multi-Higgs extension of the SM with Abelian and non-Abelian discrete symmetries which seeks to explain the origin of the masses and mixing matrices in all charge sectors.
NASA Astrophysics Data System (ADS)
Dolan, Louise; Sun, Yang
2015-06-01
We compute the partition function of four-dimensional abelian gauge theory on a general four-torus T 4 with flat metric using Dirac quantization. In addition to an symmetry, it possesses symmetry that is electromagnetic S-duality. We show explicitly how this S-duality of the 4 d abelian gauge theory has its origin in symmetries of the 6 d (2 , 0) tensor theory, by computing the partition function of a single fivebrane compactified on T 2 times T 4, which has symmetry. If we identify the couplings of the abelian gauge theory with the complex modulus of the T 2 torus , then in the small T 2 limit, the partition function of the fivebrane tensor field can be factorized, and contains the partition function of the 4 d gauge theory. In this way the symmetry of the 6d tensor partition function is identified with the S-duality symmetry of the 4d gauge partition function. Each partition function is the product of zero mode and oscillator contributions, where the acts suitably. For the 4d gauge theory, which has a Lagrangian, this product redistributes when using path integral quantization.
Asymptotically free scaling solutions in non-Abelian Higgs models
NASA Astrophysics Data System (ADS)
Gies, Holger; Zambelli, Luca
2015-07-01
We construct asymptotically free renormalization group trajectories for the generic non-Abelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.
Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems
NASA Astrophysics Data System (ADS)
Peterson, Michael; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan
There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν = n + 2 / 3 , for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2 / 3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2 / 3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν = 8 / 3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8 / 3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively. We acknowledge the Office of Research and Sponsored Programs at California State University Long Beach and Microsoft Station Q.
Abelian and non-Abelian states in ν =2 /3 bilayer fractional quantum Hall systems
NASA Astrophysics Data System (ADS)
Peterson, Michael R.; Wu, Yang-Le; Cheng, Meng; Barkeshli, Maissam; Wang, Zhenghan; Das Sarma, Sankar
2015-07-01
There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two-component FQH systems at total filling fraction ν =n +2 /3 , for integer n . Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν =n +2 /3 , including in particular the possibility of the non-Abelian Z4 parafermion state. In ν =2 /3 bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in single-component systems at ν =8 /3 , we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν =8 /3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.
Model Wavefunctions For Non-Abelian Quasiparticles
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Haldane, F. D. M.
2008-03-01
We present model wavefunctions for quasiparticle (as opposed to quasihole)excitations of the Zk parafermion sequence (Laughlin/Moore-Read/Read-Rezayi) of Fractional Quantum Hall states. These states satisfy two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together, or when two clusters of k+1 electrons are formed at different positions. For Abelian Fractional Quantum Hall states (k=1), our construction reproduces the Jain quasielectron wavefunction, and elucidates the difference between the Jain and Laughlin quasiparticle constructions. For two (or more) quasiparticles, our states differ from those constructed using Jain's method. By adding our quasiparticles to the Laughlin state, we obtain a hierarchy scheme which gives rise to a non-abelian ν=2 5 FQH state.
Non-Abelian strings and axions
Gorsky, A.; Shifman, M.; Yung, A.
2006-06-15
We address two distinct but related issues: (i) the impact of (two-dimensional) axions in a two-dimensional theory known to model confinement, the CP(N-1) model; (ii) bulk axions in four-dimensional Yang-Mills theory supporting non-Abelian strings. In the first case n, n kinks play the role of 'quarks'. They are known to be confined. We show that introduction of axions leads to deconfinement (at very large distances). This is akin to the phenomenon of wall liberation in four-dimensional Yang-Mills theory. In the second case we demonstrate that the bulk axion does not liberate confined (anti)monopoles, in contradistinction with the two-dimensional model. A novel physical effect which we observe is the axion radiation caused by monopole-antimonopole pairs attached to the non-Abelian strings.
Quantum corrections of Abelian duality transformations
NASA Astrophysics Data System (ADS)
Balog, J.; Forgács, P.; Horváth, Z.; Palla, L.
1996-02-01
A modification of the Abelian duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) σ-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat nonstandard perturbative treatment of the dual σ-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric σ-models.
Non-Abelian discrete gauge theory
NASA Astrophysics Data System (ADS)
Lee, Kai-Ming
Gauge theory with a finite gauge group (or with a gauge group that has disconnected components) is systematically studied, with emphasis on the case of a non-Abelian gauge group. An operator formalism is developed, and an order parameter is constructed that can distinguish the various phases of a gauge theory. The non-Abelian Aharonov-Bohm interactions and holonomy interactions among cosmic string loops, vortices, and charged particles are analyzed; the detection of Cheshire charge and the transfer of charge between particles and string loops (or vortex pairs) are described. Non-Abelian gauge theory on a surface with non-trivial topology is also discussed. Interactions of vortices with "handles" on the surface are discussed in detail. The electric charge of the mouth of a "wormhole" and the magnetic flux "linked" by the wormhole are shown to be non-commuting observables. This observation is used to analyze the color electric field that results when a colored object traverses a wormhole.
Non-Abelian Discrete Gauge Theory.
NASA Astrophysics Data System (ADS)
Lee, Kai-Ming
Gauge theory with a finite gauge group (or with a gauge group that has disconnected components) is systematically studied, with emphasis on the case of a non-Abelian gauge group. An operator formalism is developed, and an order parameter is constructed that can distinguish the various phases of a gauge theory. The non-Abelian Aharonov-Bohm interactions and holonomy interactions among cosmic string loops, vortices, and charged particles are analyzed; the detection of Cheshire charge and the transfer of charge between particles and string loops (or vortex pairs) are described. Non-Abelian gauge theory on a surface with non-trivial topology is also discussed. Interactions of vortices with "handles" on the surface are discussed in detail. The electric charge of the mouth of a "wormhole" and the magnetic flux "linked" by the wormhole are shown to be non-commuting observables. This observation is used to analyze the color electric field that results when a colored object traverses a wormhole.
Theory of defects in Abelian topological states
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Jian, Chao-Ming; Qi, Xiao-Liang
2013-12-01
The structure of extrinsic defects in topologically ordered states of matter is host to a rich set of universal physics. Extrinsic defects in 2+1-dimensional topological states include linelike defects, such as boundaries between topologically distinct states, and pointlike defects, such as junctions between different line defects. Gapped boundaries in particular can themselves be topologically distinct, and the junctions between them can localize topologically protected zero modes, giving rise to topological ground-state degeneracies and projective non-Abelian statistics. In this paper, we develop a general theory of point defects and gapped line defects in 2+1-dimensional Abelian topological states. We derive a classification of topologically distinct gapped boundaries in terms of certain maximal subgroups of quasiparticles with mutually bosonic statistics, called Lagrangian subgroups. The junctions between different gapped boundaries provide a general classification of point defects in topological states, including as a special case the twist defects considered in previous works. We derive a general formula for the quantum dimension of these point defects and a general understanding of their localized “parafermion” zero modes and we define a notion of projective non-Abelian statistics for them. The critical phenomena between topologically distinct gapped boundaries can be understood in terms of a general class of quantum spin chains or, equivalently, “generalized parafermion” chains. This provides a way of realizing exotic 1+1D generalized parafermion conformal field theories in condensed-matter systems.
Supersymmetry, grand unification and flavor symmetry
NASA Astrophysics Data System (ADS)
Enkhbat, Tsedenbaljir
In this thesis I have presented the findings of my research pursued during my Ph.D. study. The purpose of this thesis was to study different theoretical ideas in high energy physics model building addressed primarily towards understanding the fermion mass problem and the gauge hierarchy problem. These include: Anomalous flavor U(1) symmetry and its experimental implications, finite GUT models with discrete family symmetry, and a product GUT model in a 2D deconstructed theory space. The second and third chapters of the thesis describe our study of lepton flavor violation (LFV) and electric dipole moments (EDM) induced by a flavor-dependent anomalous U(1) gauge symmetry of string origin. The models considered also address the fermion mass hierarchy problem successfully. We have shown that the U(1) sector induces significant LFV and EDMs through the SUSY breaking parameters. These effects arise via renormalization group evolution of the parameters in the momentum regime between the string and the anomalous U(1) breaking scale. The fourth chapter of the thesis contains our work on a concrete realization of SUSY breaking using interference between the anomalous U(1) flavor gauge symmetry and a strongly coupled SU(N c), leading to the so called Split SUSY spectrum where the sfermions and the gravitino acquire masses of order 105 ÷ 108 GeV while the gauginos and the Higgsinos have masses of order 102 ÷ 103 GeV. We have calculated the leading order supergravity corrections and have presented a class of explicit models of Split SUSY which are phenomenologically consistent. In the fifth chapter I have presented models for realistic quark masses and mixings in the context of finite SU(5) GUT wherein the beta functions for the gauge and the Yukawa couplings vanish to all orders in perturbation theory. The models presented are based on non-Abelian discrete symmetries. In the case of (Z4)3 x P and A4 symmetries we have found models finite to all order of perturbation theory
Anisotropic inflation with non-abelian gauge kinetic function
Murata, Keiju; Soda, Jiro E-mail: jiro@tap.scphys.kyoto-u.ac.jp
2011-06-01
We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.
Quaternion-Octonion Analyticity for Abelian and Non-Abelian Gauge Theories of Dyons
NASA Astrophysics Data System (ADS)
Bisht, P. S.; Negi, O. P. S.
2008-06-01
Einstein-Schrödinger (ES) non-symmetric theory has been extended to accommodate the Abelian and non-Abelian gauge theories of dyons in terms of the quaternion-octonion metric realization. Corresponding covariant derivatives for complex, quaternion and octonion spaces in internal gauge groups are shown to describe the consistent field equations and generalized Dirac equation of dyons. It is also shown that quaternion and octonion representations extend the so-called unified theory of gravitation and electromagnetism to the Yang-Mill’s fields leading to two SU(2) gauge theories of internal spaces due to the presence of electric and magnetic charges on dyons.
Spontaneous symmetry breaking in 4-dimensional heterotic string
Maharana, J.
1989-07-01
The evolution of a 4-dimensional heterotic string is considered in the background of its massless excitations such as graviton, antisymmetric tensor, gauge fields and scalar bosons. The compactified bosonic coordinates are fermionized. The world-sheet supersymmetry requirement enforces Thirring-like four fermion coupling to the background scalar fields. The non-abelian gauge symmetry is exhibited through the Ward identities of the S-matrix elements. The spontaneous symmetry breaking mechanism is exhibited through the broken Ward identities. An effective 4-dimensional action is constructed and the consequence of spontaneous symmetry breaking is envisaged for the effective action. 19 refs.
Heterotic non-Abelian string of a finite length
NASA Astrophysics Data System (ADS)
Monin, S.; Shifman, M.; Yung, A.
2016-06-01
We consider non-Abelian strings in N =2 supersymmetric quantum chromodynamics (QCD) with the U (N ) gauge group and Nf=N quark flavors deformed by a mass term for the adjoint matter. This deformation breaks N =2 supersymmetry down to N =1 . Dynamics of orientational zero modes on the string world sheet are described then by C P (N -1 ) model with N =(0 ,2 ) supersymmetry. We study the string of a finite length L assuming compactification on a cylinder (periodic boundary conditions). The world-sheet theory is solved in the large-N approximation. At N =∞ we find a rich phase structure in the (L ,u ) plane where u is a deformation parameter. At large L and intermediate u we find a phase with broken Z2 N symmetry, N vacua and a mass gap. At large values of L and u still larger we have the Z2 N-symmetric phase with a single vacuum and massless fermions. In both phases N =(0 ,2 ) supersymmetry is spontaneously broken. We also observe a phase with would-be broken SU (N ) symmetry at small L (it is broken only for N =∞ ). In the latter phase the mass gap vanishes and the vacuum energy is zero in the leading 1 /N approximation. We expect that at large but finite N corrections O (1 /N ) will break N =(0 ,2 ) supersymmetry. Simultaneously, the phase transitions will become rapid crossovers. Finally we discuss how the observed rich phase structure matches the N =(2 ,2 ) limit in which the world-sheet theory has a single phase with the mass gap independent of L .
Fermion structure of non-Abelian vortices in high density QCD
Yasui, Shigehiro; Itakura, Kazunori; Nitta, Muneto
2010-05-15
We study the internal structure of a non-Abelian vortex in color superconductivity with respect to quark degrees of freedom. Stable non-Abelian vortices appear in the color-flavor-locked phase whose symmetry SU(3){sub c+L+R} is further broken to SU(2){sub c+L+R} x U(1){sub c+L+R} at the vortex cores. Microscopic structure of vortices at scales shorter than the coherence length can be analyzed by the Bogoliubov-de Gennes equation (rather than the Ginzburg-Landau equation). We obtain quark spectra from the Bogoliubov-de Gennes equation by treating the diquark gap having the vortex configuration as a background field. We find that there are massless modes (zero modes) well-localized around a vortex, in the triplet and singlet states of the unbroken symmetry SU(2){sub c+L+R} x U(1){sub c+L+R}. The velocities v{sub i} of the massless modes (i=t, s for triplet and singlet) change at finite chemical potential {mu}{ne}0, and decrease as {mu} becomes large. Therefore, low energy excitations in the vicinity of the vortices are effectively described by 1+1 dimensional massless fermions whose velocities are reduced v{sub i}<1.
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction.
Directed Abelian sandpile with multiple downward neighbors
NASA Astrophysics Data System (ADS)
Dhar, D.; Pruessner, G.; Expert, P.; Christensen, K.; Zachariou, N.
2016-04-01
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors per site, K >2 . The K =3 case is solved exactly, which extends the earlier known solution for the K =2 case. For K >2 , the avalanche clusters can have holes and side branches and are thus qualitatively different from the K =2 case where avalanche clusters are compact. However, we find that the critical exponents for K >2 are identical with those for the K =2 case, and the large-scale structure of the avalanches for K >2 tends to the K =2 case.
Non abelian hydrodynamics and heavy ion collisions
NASA Astrophysics Data System (ADS)
Calzetta, E.
2014-01-01
The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.
Non abelian hydrodynamics and heavy ion collisions
Calzetta, E.
2014-01-14
The goal of the relativistic heavy ion collisions (RHIC) program is to create a state of matter where color degrees of freedom are deconfined. The dynamics of matter in this state, in spite of the complexities of quantum chromodynamics, is largely determined by the conservation laws of energy momentum and color currents. Therefore it is possible to describe its main features in hydrodynamic terms, the very short color neutralization time notwithstanding. In this lecture we shall give a simple derivation of the hydrodynamics of a color charged fluid, by generalizing the usual derivation of hydrodynamics from kinetic theory to the non abelian case.
Directed Abelian sandpile with multiple downward neighbors.
Dhar, D; Pruessner, G; Expert, P; Christensen, K; Zachariou, N
2016-04-01
We study the directed Abelian sandpile model on a square lattice, with K downward neighbors per site, K>2. The K=3 case is solved exactly, which extends the earlier known solution for the K=2 case. For K>2, the avalanche clusters can have holes and side branches and are thus qualitatively different from the K=2 case where avalanche clusters are compact. However, we find that the critical exponents for K>2 are identical with those for the K=2 case, and the large-scale structure of the avalanches for K>2 tends to the K=2 case. PMID:27176254
Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
NASA Astrophysics Data System (ADS)
Mathai, Varghese; Sati, Hisham
2015-06-01
We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus Tn(n ≥ 2), by a noncommutative Tn-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, which is a purely noncommutative geometry phenomenon since the usual theory only has a Z2-symmetry. In particular, S-duality in this 6-dimensional higher abelian gauge theory model is shown to be, in this sense, on par with the usual 4-dimensional case.
SO(10) models with flavour symmetries: classification and examples
NASA Astrophysics Data System (ADS)
Ivanov, I. P.; Lavoura, L.
2016-10-01
Renormalizable SO(10) grand unified theory (GUT) models equipped with flavour symmetries are a popular framework for addressing the flavour puzzle. Usually, the flavour symmetry group has been an ad hoc choice, and no general arguments limiting this choice were known. In this paper, we establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) GUT with arbitrary numbers of scalar multiplets in the {{10}}, \\bar{{{126}}}, and {{120}} representations of SO(10). For each of the possible discrete non-Abelian symmetry groups, we present examples of minimal models which do not run into obvious contradiction with the phenomenological fermion masses and mixings.
Quasi-abelian and fully non-abelian gauge field copies: A classification
NASA Astrophysics Data System (ADS)
Doria, Francisco Antonio
1981-12-01
We show that a theorem by S. Solomon on quasi-abelian gauge fields extends to a full classification of ambiguous potentials for any general non-abelian field which exhibits this phenomenon. A characterization for such fields is given, as well as a criterion that distinguishes in a straightforward manner between potentials that are at least locally gauge-equivalent to a fixed canonical potential and those which are not equivalent to that potential anywhere inside a neighborhood of space-time. Our results are obtained for R4 with an arbitrary non-degenerate metric, but can be easily extended to any space-time. Three examples (due to S. Deser and F. Wilczek, S. Coleman, and T. T. Wu and C. N. Yang) are discussed in order to clarify our analysis.
Frustrated topological symmetry breaking: Geometrical frustration and anyon condensation
NASA Astrophysics Data System (ADS)
Schulz, Marc D.; Burnell, Fiona J.
2016-10-01
We study the phase diagram of a topological string-net-type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich phase diagram including both Abelian (Z2) and non-Abelian (Ising×Ising¯ ) topologically ordered phases, as well as phases with broken translational symmetry. Interestingly, one of these phases simultaneously exhibits (Abelian) topological order and long-ranged order due to translational symmetry breaking, with nontrivial interactions between excitations in the topological order and defects in the long-ranged order. We introduce a variety of effective models, valid along certain lines in the phase diagram, which can be used to characterize both topological and symmetry-breaking order in these phases and in many cases allow us to characterize the phase transitions that separate them. We use exact diagonalization and high-order series expansion to study areas of the phase diagram where these models break down and to approximate the location of the phase boundaries.
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Compère, Geoffrey
2007-03-01
The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an Abelian ideal of supertranslations. The associated charge algebra is shown to admit a non-trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.
NASA Astrophysics Data System (ADS)
Adler, Stephen L.
2015-03-01
Working with explicit examples given by the 56 representation in SU (8), and the 10 representation in SU (5), we show that symmetry breaking of a group G ⊃G1 ×G2 by a scalar in a rank three or two antisymmetric tensor representation leads to a number of distinct modular ground states. For these broken symmetry phases, the ground state is periodic in an integer divisor p of N, where N > 0 is the absolute value of the nonzero U (1) generator of the scalar component Φ that is a singlet under the simple subgroups G1 and G2. Ground state expectations of fractional powers Φ p / N provide order parameters that distinguish the different phases. For the case of period p = 1, this reduces to the usual Higgs mechanism, but for divisors N ≥ p > 1 of N it leads to a modular ground state with periodicity p, implementing a discrete Abelian symmetry group U (1) /Zp. This observation may allow new approaches to grand unification and family unification.
Preon Model and Family Replicated E_6 Unification
NASA Astrophysics Data System (ADS)
Das, Chitta Ranjan; Laperashvili, Larisa V.
2008-02-01
Previously we suggested a new preon model of composite quark-leptons and bosons with the 'flipped' E6 × ˜E6 gauge symmetry group. We assumed that preons are dyons having both hyper-electric g and hyper-magnetic ˜g charges, and these preons-dyons are confined by hyper-magnetic strings which are an N = 1 supersymmetric non-Abelian flux tubes created by the condensation of spreons near the Planck scale. In the present paper we show that the existence of the three types of strings with tensions Tk = kT0 (k = 1,2,3) producing three (and only three) generations of composite quark-leptons, also provides three generations of composite gauge bosons ('hyper-gluons') and, as a consequence, predicts the family replicated [E6]3 unification at the scale ~1017 GeV. This group of unification ha! s the possibility of breaking to the group of symmetry: [SU(3)C]3 × [SU(2)L]3 × [U(1)Y]3 × [U(1)(B-L)]3 which undergoes the breakdown to the Standard Model at lower energies. Some predictive advantages of the family replicated gauge groups of symmetry are briefly discussed.
Engineering complex topological memories from simple Abelian models
NASA Astrophysics Data System (ADS)
Wootton, James R.; Lahtinen, Ville; Doucot, Benoit; Pachos, Jiannis K.
2011-09-01
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology.
Non-Abelian Born Infeld action, geometry and supersymmetry
NASA Astrophysics Data System (ADS)
Julio Cirilo-Lombardo, Diego
2005-12-01
In this work, we propose a new non-Abelian generalization of the Born Infeld Lagrangian. It is based on a geometrical property of the Abelian Born Infeld Lagrangian in its determinantal form. Our goal is to extend the Abelian second-type Born Infeld action to the non-Abelian form preserving this geometrical property, which permits us to compute the generalized volume element as a linear combination of the components of metric and the Yang Mills energy momentum tensors. Under the BPS-like condition, the action proposed reduces to that of the Yang Mills theory, independently of the gauge group. New instanton-wormhole solution and static and spherically symmetric solution in curved spacetime for an SU(2) isotopic ansatz are solved and the N= 1 supersymmetric extension of the model is performed.
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Universal reconnection of non-Abelian cosmic strings.
Eto, Minoru; Hashimoto, Koji; Marmorini, Giacomo; Nitta, Muneto; Ohashi, Keisuke; Vinci, Walter
2007-03-01
We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings. PMID:17359147
Quantum equivalence of σ models related by non-Abelian duality transformations
NASA Astrophysics Data System (ADS)
Balázs, L. K.; Balog, J.; Forgács, P.; Mohammedi, N.; Palla, L.; Schnittger, J.
1998-03-01
Coupling constant renormalization is investigated in two dimensional σ models related by non-Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU(2) principal model and the O(3) sigma model, exhibit the same behavior as the original models. For the O(3) model also the two loop equivalence is investigated, and is found to be broken just like in the already known example of the principal model.
Engineering complex topological memories from simple Abelian models
Wootton, James R.; Lahtinen, Ville; Doucot, Benoit; Pachos, Jiannis K.
2011-09-15
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviors. An exciting proposal for quantum computation is to employ anyonic statistics to manipulate information. Since such statistical evolutions depend only on topological characteristics, the resulting computation is intrinsically resilient to errors. The so-called non-Abelian anyons are most promising for quantum computation, but their physical realization may prove to be complex. Abelian anyons, however, are easier to understand theoretically and realize experimentally. Here we show that complex topological memories inspired by non-Abelian anyons can be engineered in Abelian models. We explicitly demonstrate the control procedures for the encoding and manipulation of quantum information in specific lattice models that can be implemented in the laboratory. This bridges the gap between requirements for anyonic quantum computation and the potential of state-of-the-art technology. - Highlights: > A novel quantum memory using Abelian anyons is developed. > This uses an advanced encoding, inspired by non-Abelian anyons. > Errors are suppressed topologically, by means of single spin interactions. > An implementation with current Josephson junction technology is proposed.
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.
Probing the QCD vacuum with an Abelian chromomagnetic field: A study within an effective model
Campanelli, L.; Ruggieri, M.
2009-08-01
We study the response of the QCD vacuum to an external Abelian chromomagnetic field in the framework of a nonlocal Nambu-Jona-Lasinio model with the Polyakov loop. We use the lattice results on the deconfinement temperature of the pure gauge theory to compute the same quantity in the presence of dynamical quarks. We find a linear relationship between the deconfinement temperature with quarks and the squared root of the applied field strength, gH, in qualitative (and to some extent also quantitative) agreement with existing lattice calculations. On the other hand, we find a discrepancy on the approximate chiral symmetry restoration: while lattice results suggest the deconfinement and the chiral restoration remain linked even at a nonzero value of gH, our results are consistent with a scenario in which the two transitions are separated as gH is increased.
Harada–Tsutsui gauge recovery procedure: From Abelian gauge anomalies to the Stueckelberg mechanism
Lima, Gabriel Di Lemos Santiago
2014-02-15
Revisiting a path-integral procedure developed by Harada and Tsutsui for recovering gauge invariance from anomalous effective actions, it is shown that there are two ways to achieve gauge symmetry: one already presented by the authors, which is shown to preserve the anomaly in the sense of standard current conservation law, and another one which is anomaly-free, preserving current conservation. It is also shown that the application of the Harada–Tsutsui technique to other models which are not anomalous but do not exhibit gauge invariance allows the identification of the gauge invariant formulation of the Proca model, also done by the referred authors, with the Stueckelberg model, leading to the interpretation of the gauge invariant map as a generalization of the Stueckelberg mechanism. -- Highlights: • A gauge restoration technique from Abelian anomalous models is discussed. • It is shown that there is another way that leads to gauge symmetry restoration from such technique. • It is shown that the first gauge restoration preserves the anomaly, while the proposed second one is free from anomalies. • It is shown that the proposed gauge symmetry restoration can be identified with the Stueckelberg mechanism.
Invariant conserved currents in gravity theories: Diffeomorphisms and local gauge symmetries
NASA Astrophysics Data System (ADS)
Obukhov, Yuri N.; Rubilar, Guillermo F.
2007-12-01
Previously, we developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now generalized to the case when the local Lorentz group is replaced by an arbitrary local gauge group. The particular examples include the Maxwell and Yang-Mills fields coupled to gravity with Abelian and non-Abelian local internal symmetries and the metric-affine gravity in which the local Lorentz spacetime group is extended to the local general linear group.
Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation
Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.
2009-02-15
Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
None
2016-07-12
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ârenormalizableâ. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged âvectorâ particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of
2011-02-24
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of
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.
On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models
NASA Astrophysics Data System (ADS)
Delduc, F.; Lacroix, S.; Magro, M.; Vicedo, B.
2016-10-01
Yang-Baxter type models are integrable deformations of integrable field theories, such as the principal chiral model on a Lie group G or σ-models on (semi-)symmetric spaces G/F. The deformation has the effect of breaking the global G-symmetry of the original model, replacing the associated set of conserved charges by ones whose Poisson brackets are those of the q-deformed Poisson-Hopf algebra {{\\mathscr{U}}}q({g}). Working at the Hamiltonian level, we show how this q-deformed Poisson algebra originates from a Poisson-Lie G-symmetry. The theory of Poisson-Lie groups and their actions on Poisson manifolds, in particular the formalism of the non-abelian moment map, is reviewed. For a coboundary Poisson-Lie group G, this non-abelian moment map must obey the Semenov-Tian-Shansky bracket on the dual group {G}* , up to terms involving central quantities. When the latter vanish, we develop a general procedure linking this Poisson bracket to the defining relations of the Poisson-Hopf algebra {{\\mathscr{U}}}q({g}), including the q-Poisson-Serre relations. We consider reality conditions leading to q being either real or a phase. We determine the non-abelian moment map for Yang-Baxter type models. This enables to compute the corresponding action of G on the fields parametrising the phase space of these models.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
NASA Astrophysics Data System (ADS)
Pogrebkov, A. K.
2016-06-01
We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
Non-Abelian bosonic currents in cosmic strings
Lilley, Marc; Di Marco, Fabrizio; Martin, Jerome; Peter, Patrick
2010-07-15
A non-Abelian generalization of the neutral Witten current-carrying string model is discussed in which the bosonic current carrier belongs to a two-dimensional representation of SU(2). We find that the current-carrying solutions can be of three different kinds: either the current spans a U(1) subgroup, and in which case one is left with an Abelian current-carrying string, or the three currents are all lightlike, traveling in the same direction (only left or right movers). The third, genuinely non-Abelian situation, cannot be handled within a cylindrically symmetric framework, but can be shown to depend on all possible string Lorentz invariant quantities that can be constructed out of the phase gradients.
Non-Abelian quantum holonomy of hydrogenlike atoms
Mousolou, Vahid Azimi; Canali, Carlo M.; Sjoeqvist, Erik
2011-09-15
We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogenlike atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and are subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy and find a relation between the phase of the whole system and corresponding marginal phases. Based on the results for the model system, we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sjoeqvist et al., Phys. Rev. Lett. 85, 2845 (2000).] are generally inequivalent.
Generalized Kitaev models and extrinsic non-Abelian twist defects.
Barkeshli, Maissam; Jiang, Hong-Chen; Thomale, Ronny; Qi, Xiao-Liang
2015-01-16
We present a wide class of partially integrable lattice models with two-spin interactions which generalize the Kitaev honeycomb model. These models have a conserved quantity associated with each plaquette, conserved large loop operators on the torus, and topological degeneracy. We introduce a "slave-genon" approach which generalizes the Majorana fermion approach in the Kitaev model. The Hilbert space of our spin model can be embedded in an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular Z_{3} generalization, and we show that in a certain limit the model is analytically tractable and produces a non-Abelian topological phase with chiral parafermion edge states. PMID:25635553
Generalized Kitaev Models and Extrinsic Non-Abelian Twist Defects
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Jiang, Hong-Chen; Thomale, Ronny; Qi, Xiao-Liang
2015-01-01
We present a wide class of partially integrable lattice models with two-spin interactions which generalize the Kitaev honeycomb model. These models have a conserved quantity associated with each plaquette, conserved large loop operators on the torus, and topological degeneracy. We introduce a "slave-genon" approach which generalizes the Majorana fermion approach in the Kitaev model. The Hilbert space of our spin model can be embedded in an enlarged Hilbert space of non-Abelian twist defects, referred to as genons. In the enlarged Hilbert space, the spin model is exactly reformulated as a model of non-Abelian genons coupled to a discrete gauge field. We discuss in detail a particular Z3 generalization, and we show that in a certain limit the model is analytically tractable and produces a non-Abelian topological phase with chiral parafermion edge states.
The Hilbert scheme of points for supersingular abelian surfaces
NASA Astrophysics Data System (ADS)
Schröer, Stefan
2009-04-01
We study the geometry of Hilbert schemes of points on abelian surfaces and Beauville’s generalized Kummer varieties in positive characteristics. The main result is that, in characteristic two, the addition map from the Hilbert scheme of two points to the abelian surface is a quasifibration such that all fibers are nonsmooth. In particular, the corresponding generalized Kummer surface is nonsmooth, and minimally elliptic singularities occur in the supersingular case. We unravel the structure of the singularities in dependence of p-rank and a-number of the abelian surface. To do so, we establish a McKay Correspondence for Artin’s wild involutions on surfaces. Along the line, we find examples of canonical singularities that are not rational singularities.
Observable T{sub 7} Lepton Flavor Symmetry at the Large Hadron Collider
Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-04-01
More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T{sub 7} and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.
Observable T7 lepton flavor symmetry at the Large Hadron Collider.
Cao, Qing-Hong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-04-01
More often than not, models of flavor symmetry rely on the use of nonrenormalizable operators (in the guise of flavons) to accomplish the phenomenologically successful tribimaximal mixing of neutrinos. We show instead how a simple renormalizable two-parameter neutrino mass model of tribimaximal mixing can be constructed with the non-Abelian discrete symmetry T(7) and the gauging of B-L. This is also achieved without the addition of auxiliary symmetries and particles present in almost all other proposals. Most importantly, it is verifiable at the Large Hadron Collider.
Abelian spatial string tension in finite temperature SU(2) gauge theory
NASA Astrophysics Data System (ADS)
Sekiguchi, Takashige; Ishiguro, Katsuya
2016-09-01
We investigate Abelian and monopole contributions to spatial string tension in the deconfined phase of finite temperature SU(2) gauge theory without imposing any gauge fixing conditions. Lattice calculations of non-Abelian and Abelian spatial string tensions from the Wilson action at gauge coupling β = 2.74 and lattice volume 243 × N t (Nt = {24, 8, 6, 4, 2}) show that these string tensions agree with each other within error bars at any adopted value of Nt, which implies Abelian dominance. From measurements of non-Abelian, Abelian and monopole forces that arise from the corresponding spatial string tension, furthermore, we find the tendency that the monopole contribution to the spatial string tension can be almost as large as the non-Abelian and Abelian ones. The temperature dependence of the calculated non-Abelian and Abelian spatial string tensions allows us to conclude that the concept of dimensional reduction holds both for non-Abelian and Abelian sectors at temperatures higher than twice the critical temperature.
Correlation-induced non-Abelian quantum holonomies
NASA Astrophysics Data System (ADS)
Johansson, Markus; Ericsson, Marie; Singh, Kuldip; Sjöqvist, Erik; Williamson, Mark S.
2011-04-01
In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the Lévay geometric phase (2004 J. Phys. A: Math. Gen. 37 1821) in the case of two-qubit systems undergoing local SU(2) evolutions.
Weyl symmetric representation of SU(3) gluodynamics in abelian projection
NASA Astrophysics Data System (ADS)
Koma, Y.; Takayama, M.; Toki, H.; Ebert, D.
2001-10-01
The dual Ginzburg-Landau (DGL) theory corresponding to the SU(3) gluodynamics in Abelian projection is formulated in a Weyl symmetric way. The Weyl symmetric DGL theory can be regarded as the sum of three types of the U(1) dual Abelian Higgs (DAH) model. As an application of this approach, the hadronic flux-tube solution corresponding to the baryonic state is investigated adopting the similar techniques used in the U(1) DAH model. The string representation of the DGL theory is also discussed in a Weyl symmetric way.
Continuous symmetry measures for complex symmetry group.
Dryzun, Chaim
2014-04-01
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.
S4 flavored CP symmetry for neutrinos
NASA Astrophysics Data System (ADS)
Mohapatra, R. N.; Nishi, C. C.
2012-10-01
A generalized CP symmetry for leptons is presented where CP transformations are part of an S4 symmetry that connects different families. We study its implications for lepton mixings in a gauge model realization of the idea using a type II seesaw for neutrino masses. The model predicts maximal atmospheric mixing, nonzero θ13 and maximal Dirac phase δD=±(π)/(2).
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
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G.; Pegoraro, F.; Ceccherini, F.
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
Fujiwara, Takanori; Fukui, Takahiro; Nitta, Muneto; Yasui, Shigehiro
2011-10-01
Color superconductivity in high-density QCD exhibits the color-flavor-locked phase. To explore zero modes in the color-flavor-locked phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem to the Bogoliubov-de Gennes (BdG) Hamiltonian. From the calculation of the topological index, we find that triplet, doublet and singlet sectors of SU(2) have certain number of chiral Majorana zero modes in the limit of vanishing chemical potential. We also solve the BdG equation by the use of the series expansion to show that the number of zero modes and their chirality match the result of the index theorem. From particle-hole symmetry of the BdG Hamiltonian, we conclude that if and only if the index of a given sector is odd, one zero mode survives generically for a finite chemical potential. We argue that this result should hold nonperturbatively even in the high-density limit.
Novel Randall-Sundrum model with S3 flavor symmetry
NASA Astrophysics Data System (ADS)
Hernández, A. E. Cárcamo; Varzielas, I. de Medeiros; Neill, Nicolás A.
2016-08-01
We propose a simple and predictive model of fermion masses and mixing in a warped extra dimension, with the smallest discrete non-Abelian group S3 and the discrete symmetries Z2⊗Z4 . Standard Model fields propagate in the bulk, and the mass hierarchies and mixing angles are accounted for the fermion zero modes localization profiles, similar to the Randall-Sundrum model. To the best of our knowledge, this model is the first implementation of an S3 flavor symmetry in this type of warped extra dimension framework. Our model successfully describes the fermion masses and mixing pattern and is consistent with the current low energy fermion flavor data. The discrete flavor symmetry in our model leads to predictive mixing inspired textures, where the Cabibbo mixing arises from the down-type quark sector, whereas the up-type quark sector contributes to the remaining mixing angles.
ERIC Educational Resources Information Center
Hurst, Hunter, Ed.; And Others
1985-01-01
This document contains the fourth volume of "Today's Delinquent," an annual publication of the National Center for Juvenile Justice. This volume deals with the issue of the family and delinquency. "The Family and Delinquency" (LaMar T. Empey) systematically reviews and weighs the evidence to support prominent theories on the origins of…
Dual Ginzburg-Landau theory for confinement and chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Toki, H.; Suganuma, H.
We introduce the dual Ginzburg-Landau (DGL) theory as a low energy effective theory of QCD. We study color confinement and dynamical chiral symmetry breaking of nonperturbative QCD by using the DGL theory, where color monopole and its condensation play an essential role on the nonperturbative dynamics in the infrared region. As a result of the dual Meissner effect, the linear static quark potential, which characterizes the quark confinement, is obtained in the long distance. We investigate then the dynamical chiral symmetry breaking by using the Schwinger-Dyson equation, where the gluon propagator includes the nonperturbative effect related to monopole condensation. We find a large enhancement of the chiral-symmetry breaking when the dual Meissner effect takes place. We study the recovery of the chiral symmetry and the deconfinement at finite temperature in the DGL theory. We discuss then the essential assumption of the DGL theory, which is the abelian dominance for the infrared physics, in the maximal abelian (MA) gauge in lattice QCD. The lattice QCD simulation demonstrates that the non-abelian gluons have a finite mass of order of 1 GeV in the MA gauge. We introduce further the instanton configuration as the source of the color monopole. In the MA gauge, a monopole circles around an instanton and with the increase of the instanton density, the monopole loop connects many instantons and a complicated monopole loop covers the whole 4 dimensional space. This study indicates that instantons may be playing an essential role even for color confinement.
BCS-BEC crossover induced by a synthetic non-Abelian gauge field
NASA Astrophysics Data System (ADS)
Vyasanakere, Jayantha P.; Zhang, Shizhong; Shenoy, Vijay B.
2011-07-01
We investigate the ground state of interacting spin-(1)/(2) fermions in three dimensions at a finite density (ρ˜kF3) in the presence of a uniform non-Abelian gauge field. The gauge-field configuration (GFC) described by a vector λ≡(λx,λy,λz), whose magnitude λ determines the gauge coupling strength, generates a generalized Rashba spin-orbit interaction. For a weak attractive interaction in the singlet channel described by a small negative scattering length (kF|as|≲1), the ground state in the absence of the gauge field (λ=0) is a BCS (Bardeen-Cooper-Schrieffer) superfluid with large overlapping pairs. With increasing gauge-coupling strength, a non-Abelian gauge field engenders a crossover of this BCS ground state to a BEC (Bose-Einstein condensate) of bosons even with a weak attractive interaction that fails to produce a two-body bound state in free vacuum (λ=0). For large gauge couplings (λ/kF≫1), the BEC attained is a condensate of bosons whose properties are solely determined by the Rashba gauge field (and not by the scattering length so long as it is nonzero)—we call these bosons “rashbons.” In the absence of interactions (as=0-), the shape of the Fermi surface of the system undergoes a topological transition at a critical gauge coupling λT. For high-symmetry GFCs we show that the crossover from the BCS superfluid to the rashbon BEC occurs in the regime of λ near λT. In the context of cold atomic systems, these results make an interesting suggestion of obtaining BCS-BEC crossover through a route other than tuning the interaction between the fermions.
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.
Geometry and energy of non-Abelian vortices
Manton, Nicholas S.; Rink, Norman A.
2011-04-15
We study pure Yang-Mills theory on {Sigma}xS{sup 2}, where {Sigma} is a compact Riemann surface, and invariance is assumed under rotations of S{sup 2}. It is well known that the self-duality equations in this setup reduce to vortex equations on {Sigma}. If the Yang-Mills gauge group is SU(2), the Bogomolny vortex equations of the Abelian Higgs model are obtained. For larger gauge groups, one generally finds vortex equations involving several matrix-valued Higgs fields. Here we focus on Yang-Mills theory with gauge group SU(N)/Z{sub N} and a special reduction which yields only one non-Abelian Higgs field. One of the new features of this reduction is the fact that while the instanton number of the theory in four dimensions is generally fractional with denominator N, we still obtain an integral vortex number in the reduced theory. We clarify the relation between these two topological charges at a bundle geometric level. Another striking feature is the emergence of nontrivial lower and upper bounds for the energy of the reduced theory on {Sigma}. These bounds are proportional to the area of {Sigma}. We give special solutions of the theory on {Sigma} by embedding solutions of the Abelian Higgs model into the non-Abelian theory, and we relate our work to the language of quiver bundles, which has recently proved fruitful in the study of dimensional reduction of Yang-Mills theory.
Fibonacci anyons from Abelian bilayer quantum Hall states.
Vaezi, Abolhassan; Barkeshli, Maissam
2014-12-01
The possibility of realizing non-Abelian statistics and utilizing it for topological quantum computation (TQC) has generated widespread interest. However, the non-Abelian statistics that can be realized in most accessible proposals is not powerful enough for universal TQC. In this Letter, we consider a simple bilayer fractional quantum Hall system with the 1/3 Laughlin state in each layer. We show that interlayer tunneling can drive a transition to an exotic non-Abelian state that contains the famous "Fibonacci" anyon, whose non-Abelian statistics is powerful enough for universal TQC. Our analysis rests on startling agreements from a variety of distinct methods, including thin torus limits, effective field theories, and coupled wire constructions. We provide evidence that the transition can be continuous, at which point the charge gap remains open while the neutral gap closes. This raises the question of whether these exotic phases may have already been realized at ν=2/3 in bilayers, as past experiments may not have definitively ruled them out. PMID:25526149
Non-Abelian strings in supersymmetric Yang-Mills
Shifman, M.
2012-09-26
I give a broad review of novel phenomena discovered in certain Yang-Mills theories: non-Abelian strings and confined monopoles. Then I explain how these phenomena allow one to study strong dynamics of gauge theories in four dimensions from two-dimensional models emerging on the string world sheet.
The No-Hair Theorem for the Abelian Higgs Model
NASA Astrophysics Data System (ADS)
Lahiri, Amitabha
We consider the general procedure for proving no-hair theorems for static, spherically symmetric black holes. We apply this method to the Abelian Higgs model and find a proof of the no-hair conjecture that circumvents the objections raised against the original proof due to Adler and Pearson.
Deligne-Beilinson cohomology and Abelian link invariants: Torsion case
Thuillier, F.
2009-12-15
For the Abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral nonperturbative computation of the Chern-Simons link invariants in SO(3){approx_equal}RP{sup 3}, a toy example of a 3-manifold with torsion.
NASA Astrophysics Data System (ADS)
Koma, Y.; Koma, M.; Ilgenfritz, E.-M.; Suzuki, T.; Polikarpov, M. I.
2003-11-01
The structure of the flux-tube profile in Abelian-projected (AP) SU(2) gauge theory in the maximally Abelian gauge is studied. The connection between the AP flux tube and the classical flux-tube solution of the U(1) dual Abelian Higgs model is clarified in terms of the path-integral duality transformation. This connection suggests that the electric photon and the magnetic monopole parts of the Abelian Wilson loop can act as separate sources creating the Coulombic and the solenoidal electric field inside a flux tube. The conjecture is confirmed by a lattice simulation which shows that the AP flux tube is composed of these two contributions.
Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles
Suzuki, Tsuneo; Hasegawa, Masayasu; Ishiguro, Katsuya; Koma, Yoshiaki; Sekido, Toru
2009-09-01
The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. First, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Second, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e., the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type 1 and type 2 (dual) superconductors. These results are summarized in which the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.
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
Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges
NASA Astrophysics Data System (ADS)
Pushpa; Bisht, P. S.; Negi, O. P. S.
2011-06-01
Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) e × SU(2) m × U(1) e × U(1) m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) e × SU(2) m × U(1) e × U(1) m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)× U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ± and Z 0 bosons fields and the Higgs scalar fields.
Competing Abelian and non-Abelian topological orders in ν =1 /3 +1 /3 quantum Hall bilayers
NASA Astrophysics Data System (ADS)
Geraedts, Scott; Zaletel, Michael P.; Papić, Zlatko; Mong, Roger S. K.
2015-05-01
Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν =1 /3 +1 /3 . We first consider the Coulomb interaction at bilayer separation d , bilayer tunneling energy ΔSAS, and individual layer width w , where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν =1 /3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν =1 /3 +1 /3 systems merit further experimental study.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Chiral symmetry breaking revisited: the gap equation with lattice ingredients
Aguilar, Arlene C.
2011-05-23
We study chiral symmetry breaking in QCD, using as ingredients in the quark gap equation recent lattice results for the gluon and ghost propagators. The Ansatz employed for the quark-gluon vertex is purely non-Abelian, introducing a crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. The numerical impact of these quantities is considerable: the need to invoke confinement explicitly is avoided, and the dynamical quark masses generated are of the order of 300 MeV. In addition, the pion decay constant and the quark condensate are computed, and are found to be in good agreement with phenomenology.
Nonlinear realization of local symmetries of AdS space
Clark, T.E.; Love, S.T.; Nitta, Muneto; Veldhuis, T. ter
2005-10-15
Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of AdS{sub d+1} space due to the embedding of an AdS{sub d} brane. The resulting action is an SO(2,d) invariant AdS form of the Einstein-Hilbert action, which in addition to the AdS{sub d} gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in AdS{sub d} space.
Symmetries in the two-body problem associated to quasihomogeneous potentials
NASA Astrophysics Data System (ADS)
Mioc, Vasile
2002-09-01
The dynamics in quasihomogeneous fields (characterized by sums of homogeneous potentials) models a lot of concrete physical and astronomical situations. The two-body problem in Cartesian and standard polar coordinates, as well as in regularizing McGehee-type coordinates of both collision-blow-up kind and infinity-blow-up kind, is being tackled. The corresponding vector fields present symmetries that form isomorphic Abelian groups endowed with an idempotent structure.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
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 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.
Topologically stratified energy minimizers in a product Abelian field theory
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
Maximal Abelian gauge and a generalized BRST transformation
NASA Astrophysics Data System (ADS)
Deguchi, Shinichi; Pandey, Vipul Kumar; Mandal, Bhabani Prasad
2016-05-01
We apply a generalized Becchi-Rouet-Stora-Tyutin (BRST) formulation to establish a connection between the gauge-fixed SU (2) Yang-Mills (YM) theories formulated in the Lorenz gauge and in the Maximal Abelian (MA) gauge. It is shown that the generating functional corresponding to the Faddeev-Popov (FP) effective action in the MA gauge can be obtained from that in the Lorenz gauge by carrying out an appropriate finite and field-dependent BRST (FFBRST) transformation. In this procedure, the FP effective action in the MA gauge is found from that in the Lorenz gauge by incorporating the contribution of non-trivial Jacobian due to the FFBRST transformation of the path integral measure. The present FFBRST formulation might be useful to see how Abelian dominance in the MA gauge is realized in the Lorenz gauge.
Memory on multiple time-scales in an Abelian sandpile
NASA Astrophysics Data System (ADS)
Sokolov, Andrey; Melatos, Andrew; Kieu, Tien; Webster, Rachel
2015-06-01
We report results of a numerical analysis of the memory effects in two-dimensional Abelian sandpiles. It is found that a sandpile forgets its instantaneous configuration in two distinct stages: a fast stage and a slow stage, whose durations roughly scale as N and N2 respectively, where N is the linear size of the sandpile. We confirm the presence of the longer time-scale by an independent diagnostic based on analysing emission probabilities of a hidden Markov model applied to a time-averaged sequence of avalanche sizes. The application of hidden Markov modelling to the output of sandpiles is novel. It discriminates effectively between a sandpile time series and a shuffled control time series with the same time-averaged event statistics and hence deserves further development as a pattern-recognition tool for Abelian sandpiles.
Infrared abelian dominance and dual Higgs mechanisms in MA gauge
NASA Astrophysics Data System (ADS)
Suganuma, H.; Amemiya, K.; Ichie, H.
We study infrared abelian dominance and the dual Higgs mechanism in the maximally abelian (MA) gauge using the lattice QCD Monte Carlo simulation. In the MA gauge, the off-diagonal gluon phase tends to be random, and the off-diagonal gluon Aμ± acquires the effective mass as Moff ≅ 1.2 GeV. From the monopole current in the MA gauge, we extract the dual gluon field Bμ and estimate the dual gluon mass as mB ≅ 0.5 GeV. The QCD-monopole structure is also investigated in terms of off-diagonal gluons. From the lattice QCD in the MA gauge, the dual Ginzburg-Landau (DGL) theory can be constructed as a realistic infrared effective theory based on QCD
Non-Abelian Effects on D-Branes
Russo, Jorge G.
2008-07-28
We review different non-Abelian configurations of D-branes. We then extend the Myers dielectric effect to configurations with angular momentum. The resulting time-dependent N D0-brane bound states can be interpreted as describing rotating fuzzy ellipsoids. A similar solution exists also in the presence of a RR magnetic field, that we study in detail. We show that, for any finite N, above a certain critical angular momentum it is energetically more favorable for the bound state system to dissociate into an Abelian configuration of N D0-branes moving independently. We further study D-string configurations representing fuzzy funnels deformed by the magnetic field and by the rotational motion.
Identifying non-Abelian topological order through minimal entangled states.
Zhu, W; Gong, S S; Haldane, F D M; Sheng, D N
2014-03-01
The topological order is encoded in the pattern of long-range quantum entanglements, which cannot be measured by any local observable. Here we perform an exact diagonalization study to establish the non-Abelian topological order for topological band models through entanglement entropy measurement. We focus on the quasiparticle statistics of the non-Abelian Moore-Read and Read-Rezayi states on the lattice models with bosonic particles. We identify multiple independent minimal entangled states (MESs) in the ground state manifold on a torus. The extracted modular S matrix from MESs faithfully demonstrates the Ising anyon or Fibonacci quasiparticle statistics, including the quasiparticle quantum dimensions and the fusion rules for such systems. These findings unambiguously demonstrate the topological nature of the quantum states for these flatband models without using the knowledge of model wave functions. PMID:24655269
Braiding non-Abelian quasiholes in fractional quantum Hall states.
Wu, Yang-Le; Estienne, B; Regnault, N; Bernevig, B Andrei
2014-09-12
Quasiholes in certain fractional quantum Hall states are promising candidates for the experimental realization of non-Abelian anyons. They are assumed to be localized excitations, and to display non-Abelian statistics when sufficiently separated, but these properties have not been explicitly demonstrated except for the Moore-Read state. In this work, we apply the newly developed matrix product state technique to examine these exotic excitations. For the Moore-Read and the Z_{3} Read-Rezayi states, we estimate the quasihole radii, and determine the correlation lengths associated with the exponential convergence of the braiding statistics. We provide the first microscopic verification for the Fibonacci nature of the Z_{3} Read-Rezayi quasiholes. We also present evidence for the failure of plasma screening in the nonunitary Gaffnian wave function. PMID:25259996
Ko, P.; Tang, Yong E-mail: ytang@kias.re.kr
2015-01-01
We show that hidden sector dark matter (DM) models with local dark gauge symmetries make a natural playground for the possible γ-ray excess from the galactic center (GC). We first discuss in detail the GC γ-ray excess in a scalar dark matter (DM) model with local Z{sub 3} symmetry which was recently proposed by the present authors. Within this model, scalar DM with mass 30–70 GeV is allowed due to the newly-opened (semi-)annihilation channels of a DM pair into dark Higgs φ and/or dark photon Z' pair, and the γ-ray spectrum from the GC can be fit within this model. Then we argue that the GC gamma ray excess can be easily accommodated within hidden sector dark matter models where DM is stabilized by local gauge symmetries, due to the presence of dark Higgs (and also dark photon for Abelian dark gauge symmetry)
Ko, P.; Tang, Yong
2015-01-16
We show that hidden sector dark matter (DM) models with local dark gauge symmetries make a natural playground for the possible γ-ray excess from the galactic center (GC). We first discuss in detail the GC γ-ray excess in a scalar dark matter (DM) model with local Z{sub 3} symmetry which was recently proposed by the present authors. Within this model, scalar DM with mass 30–70 GeV is allowed due to the newly-opened (semi-)annihilation channels of a DM pair into dark Higgs ϕ and/or dark photon Z′ pair, and the γ-ray spectrum from the GC can be fit within this model. Then we argue that the GC gamma ray excess can be easily accommodated within hidden sector dark matter models where DM is stabilized by local gauge symmetries, due to the presence of dark Higgs (and also dark photon for Abelian dark gauge symmetry)
Quantum corrections of Abelian Duality Transformations in Sigma models
NASA Astrophysics Data System (ADS)
Balog, J.; Forgács, P.; Horváth, Z.; Palla, L.
1997-07-01
A review is given of a recently proposed modification of the Abelian Duality transformations guaranteeing that a (not necessarily conformally invariant) σ-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat non standard perturbative treatment of the dual σ-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric σ-models.
Global aspects of abelian duality in dimension three
NASA Astrophysics Data System (ADS)
Beasley, Chris
2014-08-01
In three dimensions, an abelian gauge field is related by duality to a free, periodic scalar field. Though usually considered on , this duality can be extended to a general three-manifold M , in which case topological features of M become important. Here I comment upon several of these features as related to the partition function on M. In a companion article, I discuss similarly the algebra of operators on a surface of genus g.
Type I non-abelian superconductors in supersymmetric gauge theories
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Eto, Minoru; Vinci, Walter
2007-11-01
Non-BPS non-Abelian vortices with Bbb CBbb P1 internal moduli space are studied in an Script N = 2 supersymmetric U(1) × SU(2) gauge theory with adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same Bbb CBbb P1 orientation is always attractive: for these reasons we interpret our model as a non-Abelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colour-flavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting Bbb CBbb P1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a Bbb CBbb P1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.
Designer non-Abelian anyon platforms: from Majorana to Fibonacci
NASA Astrophysics Data System (ADS)
Alicea, Jason; Stern, Ady
2015-12-01
The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in ‘engineered’ structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon—defects binding Majorana zero modes—and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields ‘parafermionic’ generalizations of Majorana modes and even Fibonacci anyons—the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.
Escalante, Alberto Manuel-Cabrera, J.
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. • 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.
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-12-01
A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the way ideal ground-state wave functions go to zero as various clusters of electrons are brought together. In this paper, we generalize this approach to classify multilayer FQH states. Such a classification leads to the construction of a class of non-Abelian multilayer FQH states that are closely related to ĝk parafermion conformal field theories, where ĝk is an affine simple Lie algebra. We discuss the possibility of some of the simplest of these non-Abelian states occurring in experiments on bilayer FQH systems at ν=2/3 , 4/5, 4/7, etc.
An Algorithm to Compute Abelian Subalgebras in Linear Algebras of Upper-Triangular Matrices
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
2009-08-01
This paper deals with the maximal abelian dimension of the Lie algebra hn, of n×n upper-triangular matrices. Regarding this, we obtain an algorithm which computes abelian subalgebras of hn as well as its implementation (and a computational study) by using the symbolic computation package MAPLE, where the order n of the matrices in hn is the unique input needed. Let us note that the algorithm also allows us to obtain a maximal abelian subalgebra of hn.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang; Wang, Zhenghan
2008-06-01
The classification of complex wave functions of infinite variables is an important problem since it is related to the classification of possible quantum states of matter. In this paper, we propose a way to classify symmetric polynomials of infinite variables using the pattern of zeros of the polynomials. Such a classification leads to a construction of a class of simple non-Abelian quantum Hall states which are closely related to parafermion conformal field theories.
Non-Abelian Aharonov-Bohm effect with the time-dependent gauge fields
NASA Astrophysics Data System (ADS)
Hosseini Mansoori, Seyed Ali; Mirza, Behrouz
2016-04-01
We investigate the non-Abelian Aharonov-Bohm (AB) effect for time-dependent gauge fields. We prove that the non-Abelian AB phase shift related to time-dependent gauge fields, in which the electric and magnetic fields are written in the adjoint representation of SU (N) generators, vanishes up to the first order expansion of the phase factor. Therefore, the flux quantization in a superconductor ring does not appear in the time-dependent Abelian or non-Abelian AB effect.
Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum
NASA Astrophysics Data System (ADS)
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 (mH) to the gauge-field mass (mA) . 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.
Symmetric solitonic excitations of the (1 + 1)-dimensional Abelian-Higgs classical vacuum.
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.
Strong-weak coupling duality in non-abelian gauge theories
NASA Astrophysics Data System (ADS)
Ferrari, Frank
1997-05-01
This is a general introduction to electric-magnetic duality in non-abelian gauge theories. In chapter I, I review the general ideas which led in the late 70s to the idea of electric/magnetic duality in quantum field theory. In chapters II and III, I focus mainly on N=2 supersymmetric theories. I present the lagrangians and explain in more or less detail the non-renormalization theorems, rigid special geometry, supersymmetric instanton calculus, charge fractionization, the semiclassical theory of monopoles, duality in Maxwell theory and the famous Seiberg-Witten solution. I discuss various physical applications, as electric charge confinement, chiral symmetry breaking or non-trivial superconformal theories in four dimensions. In Section II.3 new material is presented, related to the computation of the eta invariant of certain Dirac operators coupled minimally to non-trivial monopole field configurations. I explain how these invariants can be obtained exactly by a one-loop calculation in a suitable N=2 supersymmetric gauge theory. This is an unexpected application of the holomorphy properties of N=2 supersymmetry, and constitutes a tremendous simplification of the usual computation. An expanded version of these new results will be published soon.
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
NASA Astrophysics Data System (ADS)
Bazavov, A.; Meurice, Y.; Tsai, S.-W.; Unmuth-Yockey, J.; Zhang, Jin
2015-10-01
We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1 +1 )-dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling βp l=1 /g2 and small values of the scalar self-coupling λ . In the opposite limit of infinitely large λ , the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of μ has consequences only if we have an external electric field, g2=0 or an explicit gauge symmetry breaking. The time-continuum limit of the blocked transfer matrix can be obtained numerically and, for g2=0 and a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large on-site repulsion. We extend this procedure for finite βp l and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Planar limit of orientifold field theories and emergent center symmetry
NASA Astrophysics Data System (ADS)
Armoni, Adi; Shifman, Mikhail; Ünsal, Mithat
2008-02-01
We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R3×S1 where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has ZN center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from ZN symmetric to ZN broken phase applies. At the Lagrangian level the orientifold theories have at most a Z2 center. We discuss how the full ZN center symmetry dynamically emerges in the orientifold theories in the limit N→∞. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Planar limit of orientifold field theories and emergent center symmetry
Armoni, Adi; Shifman, Mikhail; Uensal, Mithat
2008-02-15
We consider orientifold field theories [i.e., SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations] on R{sub 3}xS{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills theory. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N{yields}{infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
Armoni, Adi; Shifman, Mikhail; Unsal, Mithat
2007-12-05
We consider orientifold field theories (i.e. SU(N) Yang-Mills theories with fermions in the two-index symmetric or antisymmetric representations) on R{sub 3} x S{sub 1} where the compact dimension can be either temporal or spatial. These theories are planar equivalent to supersymmetric Yang-Mills. The latter has Z{sub N} center symmetry. The famous Polyakov criterion establishing confinement-deconfinement phase transition as that from Z{sub N} symmetric to Z{sub N} broken phase applies. At the Lagrangian level the orientifold theories have at most a Z{sub 2} center. We discuss how the full Z{sub N} center symmetry dynamically emerges in the orientifold theories in the limit N {yields} {infinity}. In the confining phase the manifestation of this enhancement is the existence of stable k-strings in the large-N limit of the orientifold theories. These strings are identical to those of supersymmetric Yang-Mills theories. We argue that critical temperatures (and other features) of the confinement-deconfinement phase transition are the same in the orientifold daughters and their supersymmetric parent up to 1/N corrections. We also discuss the Abelian and non-Abelian confining regimes of four-dimensional QCD-like theories.
Non-Abelian k-vortex dynamics in Script N = 1* theory and its gravity dual
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Kumar, S. Prem
2008-12-01
We study magnetic flux tubes in the Higgs vacuum of the Script N = 1* mass deformation of SU(Nc), Script N = 4 SYM and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc we identify a ``colour-flavour locked'' symmetry, SO(3)C+F which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a Bbb ZNc-valued magnetic flux, with winding, 0 < k < Nc. These k-strings spontaneously break SO(3)C+F to U(1)C+F resulting in an S2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric Bbb CBbb P1 model with a theta angle θ1+1 = k(Nc-k)θ3+1 where θ3+1 is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law Tk propto k(Nc-k) for large Nc. In the large Nc IIB string dual, the SO(3)C+F symmetry is manifest in the geometry interpolating between AdS5 × S5 and the interior metric due to a single D5-brane carrying D3-brane charge. We identify candidate k-vortices as expanded probe D3-branes formed from a collection of k D-strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S-duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in Script N = 1* theory in the large Nc limit.
Entanglement entropy and nonabelian gauge symmetry
NASA Astrophysics Data System (ADS)
Donnelly, William
2014-11-01
Entanglement entropy has proven to be an extremely useful concept in quantum field theory. Gauge theories are of particular interest, but for these systems the entanglement entropy is not clearly defined because the physical Hilbert space does not factor as a tensor product according to regions of space. Here we review a definition of entanglement entropy that applies to abelian and nonabelian lattice gauge theories. This entanglement entropy is obtained by embedding the physical Hilbert space into a product of Hilbert spaces associated to regions with boundary. The latter Hilbert spaces include degrees of freedom on the entangling surface that transform like surface charges under the gauge symmetry. These degrees of freedom are shown to contribute to the entanglement entropy, and the form of this contribution is determined by the gauge symmetry. We test our definition using the example of two-dimensional Yang-Mills theory, and find that it agrees with the thermal entropy in de Sitter space, and with the results of the Euclidean replica trick. We discuss the possible implications of this result for more complicated gauge theories, including quantum gravity.
Flavor symmetry breaking and meson masses
Bhagwat, Mandar S.; Roberts, Craig D.; Chang Lei; Liu Yuxin; Tandy, Peter C.
2007-10-15
The axial-vector Ward-Takahashi identity is used to derive mass formulas for neutral pseudoscalar mesons. Flavor symmetry breaking entails nonideal flavor content for these states. Adding that the {eta}{sup '} is not a Goldstone mode, exact chiral-limit relations are developed from the identity. They connect the dressed-quark propagator to the topological susceptibility. It is confirmed that in the chiral limit the {eta}{sup '} mass is proportional to the matrix element which connects this state to the vacuum via the topological susceptibility. The implications of the mass formulas are illustrated using an elementary dynamical model, which includes an Ansatz for that part of the Bethe-Salpeter kernel related to the non-Abelian anomaly. In addition to the current-quark masses, the model involves two parameters, one of which is a mass-scale. It is employed in an analysis of pseudoscalar- and vector-meson bound-states. While the effects of SU(N{sub f}=2) and SU(N{sub f}=3) flavor symmetry breaking are emphasized, the five-flavor spectra are described. Despite its simplicity, the model is elucidative and phenomenologically efficacious; e.g., it predicts {eta}-{eta}{sup '} mixing angles of {approx}-15 deg. and {pi}{sup 0}-{eta} angles of {approx}1 deg.
Hyperscaling violation and electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Elander, Daniel; Lawrance, Robert; Piai, Maurizio
2015-08-01
We consider a class of simplified models of dynamical electroweak symmetry breaking built in terms of their five-dimensional weakly-coupled gravity duals, in the spirit of bottom-up holography. The sigma-model consists of two abelian gauge bosons and one real, non-charged scalar field coupled to gravity in five dimensions. The scalar potential is a simple exponential function of the scalar field. The background metric resulting from solving the classical equations of motion exhibits hyperscaling violation, at least at asymptotically large values of the radial direction. We study the spectrum of scalar composite states of the putative dual field theory by fluctuating the sigma-model scalars and gravity, and discuss in which cases we find a parametrically light scalar state in the spectrum. We model the spontaneous breaking of the (weakly coupled) gauge symmetry to the diagonal subgroup by the choice of IR boundary conditions. We compute the mass spectrum of spin-1 states, and the precision electroweak parameter S as a function of the hyperscaling coefficient. We find a general bound on the mass of the lightest spin-1 resonance, by requiring that the indirect bounds on the precision parameters be satisfied, that implies that precision electroweak physics excludes the possibility of a techni-rho meson with mass lighter than several TeV.
Holographic Symmetries and Generalized Order Parameters for Topological Matter
NASA Astrophysics Data System (ADS)
Cobanera, Emilio; Ortiz, Gerardo; Nussinov, Zohar
2013-03-01
We introduce a universally applicable method, based on the bond-algebraic theory of dualities, to search for generalized order parameters in a wide variety of non-Landau systems, including topologically ordered matter. To this end we introduce the key notion of holographic symmetry. It reflects situations in which global symmetries become exact boundary symmetries under a duality mapping. Holographic symmetries are naturally related to edge modes and localization. The utility of our approach is illustrated by presenting a systematic derivation of generalized order parameters for pure and matter-coupled Abelian gauge theories and (extended) toric codes. Also we introduce a many-body extension of the Kitaev wire, the gauged Kitaev wire, and exploit holographic symmetries and dualities to describe its phase diagram, generalized order parameter, and edge states. [arXiv:1211.0564] This work was supported by the Dutch Science Foundation NWO/FOM and an ERC Advanced Investigator grant, and, in part, under grants No. NSF PHY11-25915 and CMMT 1106293.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
Veneziano amplitudes, spin chains and Abelian reduction of QCD
NASA Astrophysics Data System (ADS)
Kholodenko, Arkady
2009-05-01
Although QCD can be treated perturbatively in the high energy limit, lower energies require uses of nonperturbative methods such as ADS/CFT and/or Abelian reduction. These methods are not equivalent. While the first is restricted to supersymmetric Yang-Mills model with number of colors going to infinity, the second is not restricted by requirements of supersymmetry and is designed to work in the physically realistic limit of a finite number of colors. In this paper we provide arguments in favor of the Abelian reduction methods. This is achieved by further developing results of our recent works re-analyzing Veneziano and Veneziano-like amplitudes and the models associated with these amplitudes. It is shown, that the obtained new partition function for these amplitudes can be mapped exactly into that for the Polychronakos-Frahm (P-F) spin chain model recoverable from the Richardon-Gaudin (R-G) XXX spin chain model originally designed for treatments of the BCS-type superconductivity. Because of this, it is demonstrated that the obtained mapping is compatible with the method of Abelian reduction. The R-G model is recovered from the asymptotic (WKB-type) solutions of the rational Knizhnik-Zamolodchikov (K-Z) equation. Linear independence of these solutions is controlled by determinants whose explicit form (up to a constant) coincides with Veneziano (or Veneziano-like) amplitudes. In the simplest case, the determinantal conditions coincide with those discovered by Kummer in the 19th century. Kummer's results admit physical interpretation by relating determinantal formula(s) to Veneziano-like amplitudes. Furthermore, these amplitudes can be interpreted as Poisson-Dirichlet distributions playing a central role in the stochastic theory of random coagulation-fragmentation processes. Such an interpretation is complementary to that known for the Lund model widely used for the description of coagulation-fragmentation processes in QCD.
On spectral synthesis on zero-dimensional Abelian groups
Platonov, S S
2013-09-30
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 H⊆C(G) is said to be an invariant subspace if it is invariant with respect to the translations τ{sub y}:f(x)↦f(x+y), y∈G. In the paper, it is proved that any invariant subspace H admits spectral synthesis, that is, H coincides with the closed linear span of the characters of G belonging to H. Bibliography: 25 titles.
The Abelian Sandpile Model on a Random Binary Tree
NASA Astrophysics Data System (ADS)
Redig, F.; Ruszel, W. M.; Saada, E.
2012-06-01
We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar and Majumdar, we prove exponential decay of correlations, and in a small supercritical region (i.e., where the branching process survives with positive probability) exponential decay of avalanche sizes. This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes. Our main technical tools are: (1) A recursion for the ratio between the numbers of weakly and strongly allowed configurations which is proved to have a well-defined stochastic solution; (2) quenched and annealed estimates of the eigenvalues of a product of n random transfer matrices.
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.
Abelian tensor hierarchy in 4D, N = 1 superspace
NASA Astrophysics Data System (ADS)
Becker, Katrin; Becker, Melanie; Linch, William D.; Robbins, Daniel
2016-03-01
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N =1superspaceandconstructitsChern-Simons-likeinvariants. Whenspecializedtothe case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N = 1 superfields.
Non-Abelian gauge invariance and the infrared approximation
Cho, H.h.; Fried, H.M.; Grandou, T.
1988-02-15
Two constructions are given of infrared approximations, defined by a nonlocal configuration-space restrictions, which preserve the local, non-Abelian gauge invariance of SU(N) two-dimensional QCD (QCD/sub 2/). These continuum infrared methods are used to estimate the quenched order parameter
Exact integration of height probabilities in the Abelian Sandpile model
NASA Astrophysics Data System (ADS)
Caracciolo, Sergio; Sportiello, Andrea
2012-09-01
The height probabilities for the recurrent configurations in the Abelian Sandpile model on the square lattice have analytic expressions, in terms of multidimensional quadratures. At first, these quantities were evaluated numerically with high accuracy and conjectured to be certain cubic rational-coefficient polynomials in π-1. Later their values were determined by different methods. We revert to the direct derivation of these probabilities, by computing analytically the corresponding integrals. Once again, we confirm the predictions on the probabilities, and thus, as a corollary, the conjecture on the average height, <ρ> = 17/8.
Tensor network states and algorithms in the presence of a global SU(2) symmetry
NASA Astrophysics Data System (ADS)
Singh, Sukhwinder; Vidal, Guifre
2012-11-01
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g., with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely, (i) [Singh, Pfeifer, and Vidal, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.050301 82, 050301 (2010)] and (ii) [Singh, Pfeifer, and Vidal, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.115125 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible, and multiplicity free, acting as a global internal symmetry. Then, in (ii) we described the implementation of Abelian group symmetries in much more detail, considering a U(1) symmetry (e.g., conservation of global particle number) as a concrete example. In this paper, we describe the implementation of non-Abelian group symmetries in great detail. For concreteness, we consider an SU(2) symmetry (e.g., conservation of global quantum spin). Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we
Non-Abelian dynamics in the resonant decay of the Higgs after inflation
Enqvist, Kari; Nurmi, Sami; Rusak, Stanislav E-mail: sami.nurmi@helsinki.fi
2014-10-01
We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.
Non-Abelian topological insulators from an array of quantum wires
NASA Astrophysics Data System (ADS)
Sagi, Eran; Oreg, Yuval
2014-11-01
We suggest a construction of a large class of topological states using an array of quantum wires. First, we show how to construct a Chern insulator using an array of alternating wires that contain electrons and holes, correlated with an alternating magnetic field. This is supported by semiclassical arguments and a full quantum-mechanical treatment of an analogous tight-binding model. We then show how electron-electron interactions can stabilize fractional Chern insulators (Abelian and non-Abelian). In particular, we construct a non-Abelian Z3 parafermion state. Our construction is generalized to wires with alternating spin-orbit couplings, which give rise to integer and fractional (Abelian and non-Abelian) topological insulators. The states we construct are effectively two dimensional, and are therefore less sensitive to disorder than one-dimensional systems. The possibility of experimental realization of our construction is addressed.
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.
Nonzero θ13 for neutrino mixing in a supersymmetric B-L gauge model with T7 lepton flavor symmetry
NASA Astrophysics Data System (ADS)
Cao, Qing-Hong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-10-01
We discuss how θ13≠0 is accommodated in a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T7 in the context of a supersymmetric extension of the standard model with gauged U(1)B-L. We predict a correlation between θ13 and θ23, as well as the effective neutrino mass mee in neutrinoless double beta decay.
Matrix product states and the non-Abelian rotor model
NASA Astrophysics Data System (ADS)
Milsted, Ashley
2016-04-01
We use uniform matrix product states to study the (1 +1 )D O (2 ) and O (4 ) rotor models, which are equivalent to the Kogut-Susskind formulation of matter-free non-Abelian lattice gauge theory on a "Hawaiian earring" graph for U (1 ) and S U (2 ), respectively. Applying tangent space methods to obtain ground states and determine the mass gap and the β function, we find excellent agreement with known results, locating the Berezinskii-Kosterlitz-Thouless transition for O (2 ) and successfully entering the asymptotic weak-coupling regime for O (4 ). To obtain a finite local Hilbert space, we truncate in the space of generalized Fourier modes of the gauge group, comparing the effects of different cutoff values. We find that higher modes become important in the crossover and weak-coupling regimes of the non-Abelian theory, where entanglement also suddenly increases. This could have important consequences for tensor network state studies of Yang-Mills on higher-dimensional graphs.
Contraction of broken symmetries via Kac-Moody formalism
NASA Astrophysics Data System (ADS)
Daboul, Jamil
2006-08-01
I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard two-dimensional Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by H2, gets reduced by the symmetry breaking term, defined by the Hamiltonian H(β )=(1/2m)(p12+p22)-α/r-βr-1/2cos((φ-γ)/2). For this H(β ) I define two symmetry loop algebras Li(β), i =1,2, by choosing the "basic generators" differently. These Li(β) can be mapped isomorphically onto subalgebras of H2, of codimension two or three, revealing the reduction of symmetry. Both factor algebras Li(β)/Ii(E,β), relative to the corresponding energy-dependent ideals Ii(E,β), are isomorphic to so(3) and so(2,1) for E <0 and E >0, respectively, just as for the pure Kepler case. However, they yield two different nonstandard contractions as E →0, namely to the Heisenberg-Weyl algebra h3=w1 or to an Abelian Lie algebra, instead of the Euclidean algebra e(2) for the pure Kepler case. The above-noted example suggests a general procedure for defining generalized contractions, and also illustrates the "deformation contraction hysteresis," where contraction which involves two contraction parameters can yield different contracted algebras, if the limits are carried out in different order.
Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications
NASA Astrophysics Data System (ADS)
Blaszczyk, Michael; Oehlmann, Paul-Konstantin
2016-04-01
We are considering the class of heterotic N=(2,2) Landau-Ginzburg orbifolds with 9 fields corresponding to A 1 9 Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with N=1 , 2 and 4 supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a Z_3 orbifold on an E6 lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also in the smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric Z_3× Z_{3,free} orbifold regime.
Baryogenesis from symmetry principle
NASA Astrophysics Data System (ADS)
Fong, Chee Sheng
2016-01-01
In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identify the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.
Dual Ginzburg-Landau Theory for Confinement and Chiral Symmetry Breaking
NASA Astrophysics Data System (ADS)
Toki, H.; Suganuma, H.
We introduce the dual Ginzburg-Landau (DGL) theory as a low energy effective theory of QCD. We study color confinement and dynamical chiral symmetry breaking of nonperturbative QCD by using the DGL theory, where color monopole and its condensation play an essential role on the nonpertubative dynamics in the infrared region. As a result of the dual Meissner effect, the linear static quark potential, which characterizes the quark confinement, is obtained in the long distance. We investigate then the dynamical chiral symmetry breaking by using the Schwinger-Dyson equation, where the gluon propagator includes the nonperturbative effect related to monopole condensation. We find a large enhancement of the chiral-symmetry breaking when the dual Meissner effect takes place. We study the recovery of the chiral symmetry and the deconfinement at finite temperature in the DGL theory. We discuss then the essential assumption of the DGL theory, which is the abelian dominance for the infrared physics, in the maximal abelian (MA) gauge in lattice QCD. The lattice QCD simulation demonstrates that the non-abelian gluons have a finite mass of order of 1 GeV in the MA gauge. We introduce further the instanton configuration as the source of the color monopole. In the MA gauge, a monopole circles around an instanton and with the increase of the instanton density, the monopole loop connects many instantons and a complicated monopole loop covers the whole 4 dimensional space. This study indicates that the instantons may be playing an essential role even for color confinement.
Internal symmetry in protein structures: prevalence, functional relevance and evolution.
Balaji, Santhanam
2015-06-01
Symmetry has been found at various levels of biological organization in the protein structural universe. Numerous evolutionary studies have proposed connections between internal symmetry within protein tertiary structures, quaternary associations and protein functions. Recent computational methods, such as SymD and CE-Symm, facilitate a large-scale detection of internal symmetry in protein structures. Based on the results from these methods, about 20% of SCOP folds, superfamilies and families are estimated to have structures with internal symmetry (Figure 1d). All-β and membrane proteins fold classes contain a relatively high number of unique instances of internal symmetry. In addition to the axis of symmetry, anecdotal evidence suggests that, the region of connection or contact between symmetric units could coincide with functionally relevant sites within a fold. General principles that underlie protein internal symmetry and their connections to protein structural integrity and functions remain to be elucidated.
NASA Astrophysics Data System (ADS)
Lu, Yuan-Ming; Vishwanath, Ashvin
2016-04-01
We study (2+1)-dimensional phases with topological order, such as fractional quantum Hall states and gapped spin liquids, in the presence of global symmetries. Phases that share the same topological order can then differ depending on the action of symmetry, leading to symmetry-enriched topological (SET) phases. Here, we present a K -matrix Chern-Simons approach to identify distinct phases with Abelian topological order, in the presence of unitary or antiunitary global symmetries. A key step is the identification of a smooth edge sewing condition that is used to check if two putative phases are indeed distinct. We illustrate this method by classifying Z2 topological order (Z2 spin liquids) in the presence of an internal Z2 global symmetry for which we find six distinct phases. These include two phases with an unconventional action of symmetry that permutes anyons leading to symmetry-protected Majorana edge modes. Other routes to realizing protected edge states in SET phases are identified. Symmetry-enriched Laughlin states and double-semion theories are also discussed. Somewhat surprisingly, we observe that (i) gauging the global symmetry of distinct SET phases leads to topological orders with the same total quantum dimension, and (ii) a pair of distinct SET phases can yield the same topological order on gauging the symmetry.
Symmetry in Mathematics Learning.
ERIC Educational Resources Information Center
Dreyfus, Tommy; Eisenberg, Theodore
1989-01-01
Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits
NASA Astrophysics Data System (ADS)
Mezzacapo, A.; Rico, E.; Sabín, C.; Egusquiza, I. L.; Lamata, L.; Solano, E.
2015-12-01
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.
Non-Abelian SU(2) Lattice Gauge Theories in Superconducting Circuits.
Mezzacapo, A; Rico, E; Sabín, C; Egusquiza, I L; Lamata, L; Solano, E
2015-12-11
We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure SU(2) gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms. PMID:26705616
Study of the Gribov region in Euclidean Yang-Mills theories in the maximal Abelian gauge
Capri, M. A. L.; Gomez, A. J.; Lemes, V. E. R.; Sobreiro, R. F.; Sorella, S. P.
2009-01-15
The properties of the Gribov region in SU(2) Euclidean Yang-Mills theories in the maximal Abelian gauge are investigated. This region turns out to be bounded in all off-diagonal directions, while it is unbounded along the diagonal one. The soft breaking of the Becchi-Rouet-Stora-Tyutin invariance due to the restriction of the domain of integration in the path integral to the Gribov region is scrutinized. Owing to the unboundedness in the diagonal direction, the invariance with respect to Abelian transformations is preserved, a property which is at the origin of the local U(1) Ward identity of the maximal Abelian gauge.
New CMB constraints for Abelian Higgs cosmic strings
NASA Astrophysics Data System (ADS)
Lizarraga, Joanes; Urrestilla, Jon; Daverio, David; Hindmarsh, Mark; Kunz, Martin
2016-10-01
We present cosmic microwave background (CMB) power spectra from recent numerical simulations of cosmic strings in the Abelian Higgs model and compare them to CMB power spectra measured by Planck. We obtain revised constraints on the cosmic string tension parameter Gμ. For example, in the ΛCDM model with the addition of strings and no primordial tensor perturbations, we find Gμ < 2.0 × 10‑7 at 95% confidence, about 20% lower than the value obtained from previous simulations, which had 1/64 of the spatial volume. The increased computational volume also makes it possible to simulate fully the physical equations of motion, in which the string cores shrink in comoving coordinates. We find however that this, and the larger dynamic range, changes the amplitude of the power spectra by only about 10%. The main cause of the stronger constraints on Gμ is instead an improved treatment of the string evolution across the radiation-matter transition.
Non-Abelian gerbes and enhanced Leibniz algebras
NASA Astrophysics Data System (ADS)
Strobl, Thomas
2016-07-01
We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e., dropping eventual contributions that can be added in particular space-time dimensions only such as higher Chern-Simons terms. After appropriate field redefinitions it coincides with a truncation of the Samtleben-Szegin-Wimmer action. In the process one sees explicitly how the existence of a gauge-invariant functional enforces that the most general semistrict Lie 2-algebra describing the bundle of a non-Abelian gerbe gets reduced to a very particular structure, which, after the field redefinition, can be identified with the one of an enhanced Leibniz algebra. This is the first step towards a systematic construction of such functionals for higher gauge theories, with kinetic terms for a tower of gauge fields up to some highest form degree p , solved here for p =2 .
Matrix model for non-Abelian quantum Hall states
NASA Astrophysics Data System (ADS)
Dorey, Nick; Tong, David; Turner, Carl
2016-08-01
We propose a matrix quantum mechanics for a class of non-Abelian quantum Hall states. The model describes electrons which carry an internal SU(p ) spin. The ground states of the matrix model include spin-singlet generalizations of the Moore-Read and Read-Rezayi states and, in general, lie in a class previously introduced by Blok and Wen. The effective action for these states is a U(p ) Chern-Simons theory. We show how the matrix model can be derived from quantization of the vortices in this Chern-Simons theory and how the matrix model ground states can be reconstructed as correlation functions in the boundary WZW model.
Tachyons on Dp-branes from abelian Higgs sphalerons
NASA Astrophysics Data System (ADS)
Brihaye, Yves; Hartmann, Betti
2005-11-01
We consider the abelian Higgs model in a (p+2)-dimensional space time with topology Bbb Mp+1 × S1 as a field theoretical toy model for tachyon condensation on Dp-branes. The theory has periodic sphaleron solutions with the normal mode equations resembling Lamé-type equations. These equations are quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson mass ratio and hence a finite number of algebraic normal modes can be computed explicitely. We calculate the tachyon potential for two different values of the Higgs- to gauge boson mass ratio and show that in comparison to previously studied pure scalar field models an exact cancellation between the negative energy contribution at the minimum of the tachyon potential and the brane tension is possible for the simplest truncation in the expansion about the field around the sphaleron. This gives further evidence for the correctness of Sen's conjecture.
Vortex operator and BKT transition in Abelian duality
NASA Astrophysics Data System (ADS)
Chern, Tong
2016-04-01
We give a new simple derivation for the sine-Gordon description of Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Our derivation is simpler than traditional derivations. Besides, our derivation is a continuous field theoretic derivation by using path integration, different from the traditional derivations which are based on lattice theory or based on Coulomb gas model. Our new derivation relies on Abelian duality of two dimensional quantum field theory. By utilizing this duality in path integration, we find that the vortex configurations are naturally mapped to exponential operators in dual description. Since these operators are the vortex operators that can create vortices, the sine-Gordon description then naturally follows. Our method may be useful for the investigation to the BKT physics of superconductors.
Simulation of non-Abelian gauge theories with optical lattices.
Tagliacozzo, L; Celi, A; Orland, P; Mitchell, M W; Lewenstein, M
2013-01-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors). PMID:24162080
Simulation of non-Abelian gauge theories with optical lattices
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Orland, P.; Mitchell, M. W.; Lewenstein, M.
2013-10-01
Many phenomena occurring in strongly correlated quantum systems still await conclusive explanations. The absence of isolated free quarks in nature is an example. It is attributed to quark confinement, whose origin is not yet understood. The phase diagram for nuclear matter at general temperatures and densities, studied in heavy-ion collisions, is not settled. Finally, we have no definitive theory of high-temperature superconductivity. Though we have theories that could underlie such physics, we lack the tools to determine the experimental consequences of these theories. Quantum simulators may provide such tools. Here we show how to engineer quantum simulators of non-Abelian lattice gauge theories. The systems we consider have several applications: they can be used to mimic quark confinement or to study dimer and valence-bond states (which may be relevant for high-temperature superconductors).
Abelian Hidden Sectors at a GeV
Morrissey, David E.; Poland, David; Zurek, Kathryn; /Fermilab /Michigan U.
2009-04-16
We discuss mechanisms for naturally generating GeV-scale hidden sectors in the context of weak-scale supersymmetry. Such low mass scales can arise when hidden sectors are more weakly coupled to supersymmetry breaking than the visible sector, as happens when supersymmetry breaking is communicated to the visible sector by gauge interactions under which the hidden sector is uncharged, or if the hidden sector is sequestered from gravity-mediated supersymmetry breaking. We study these mechanisms in detail in the context of gauge and gaugino mediation, and present specific models of Abelian GeV-scale hidden sectors. In particular, we discuss kinetic mixing of a U(1){sub x} gauge force with hypercharge, singlets or bi-fundamentals which couple to both sectors, and additional loop effects. Finally, we investigate the possible relevance of such sectors for dark matter phenomenology, as well as for low- and high-energy collider searches.
Symmetry Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
Non-Abelian quantum Hall states of fermions and bosons
NASA Astrophysics Data System (ADS)
Read, Nicholas
2007-03-01
In a non-Abelian quantum Hall state, there are types of elementary excitations or quasiparticles that obey non-Abelian statistics. This is an extension of the idea of fractional statistics that means that when several of these quasiparticles are present in the system and are well-separated at well-defined positions, there is a degenerate space of lowest-energy states. When the quasiparticles are then exchanged adiabatically, the result is a matrix operation on this space of states. Greg Moore and the author^1 introduced this idea to condensed matter physics in 1991. They proposed a basic example called the Moore-Read Pfaffian state. The physics of the existence of the degenerate states for the quasiparticles in this system can be understood by viewing it as a px-ipy paired state of composite fermions, in which quasiparticles are hc/2e vortices that carry Majorana fermion zero modes. This state is expected to be realized in the filling factor ν=5/2 fractional quantum Hall (FQH) state. In later work, a series (labeled by an integer k) of ``parafermion'' states was proposed^2. This talk will review these ideas, and describe recent numerical work that strongly supports the idea that the k=3 member of the sequence occurs in the filling factor 12/5 FQH state for electrons^3, and also^4 in a system of bosons, such as rotating cold atoms, at filling factor 3/2. It will also describe recent analytical results^5 on the explicit quasihole trial wavefunctions of the parafermion states. 1. G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991). 2. N. Read and E. Rezayi, Phys. Rev. B 59, 8084 (1999). 3. E.H. Rezayi and N. Read, cond-mat/0608346. 4. E.H. Rezayi, N. Read, and N.R. Cooper, Phys. Rev. Lett.95, 160404 (2005). 5. N. Read, Phys. Rev. B 73, 245334 (2006).
The Two-Body Problem in the Point Mass Approximation Field. IV. Symmetries
NASA Astrophysics Data System (ADS)
Mioc, Vasile; Csillik, Iharka
The only fields for which the correctness of the point-mass representation (Newton's theorem) can be proved are those featured by potentials of the form A/r+Br2. The two-body problem in such a field is tackled from the only standpoint of symmetries. The motion equations, written in Cartesian or polar coordinates, present nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. It is the same for McGehee-type coordinates that extend the phase space to collision or escape. All these groups are proved to be isomorphic. Expressed in Levi-Civita collision-regularizing coordinates, the vector field of the problem exhibits symmetries that form a sixteen-element group with the same characteristics.
Chiral symmetry breaking with lattice propagators
Aguilar, A. C.; Papavassiliou, J.
2011-01-01
We study chiral symmetry breaking using the standard gap equation, supplemented with the infrared-finite gluon propagator and ghost dressing function obtained from large-volume lattice simulations. One of the most important ingredients of this analysis is the non-Abelian quark-gluon vertex, which controls the way the ghost sector enters into the gap equation. Specifically, this vertex introduces a numerically crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. This latter quantity satisfies its own, previously unexplored, dynamical equation, which may be decomposed into individual integral equations for its various form factors. In particular, the scalar form factor is obtained from an approximate version of the 'one-loop dressed' integral equation, and its numerical impact turns out to be rather considerable. The detailed numerical analysis of the resulting gap equation reveals that the constituent quark mass obtained is about 300 MeV, while fermions in the adjoint representation acquire a mass in the range of (750-962) MeV.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-07-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
Manifestation of a non-Abelian Berry phase in a p -type semiconductor system
NASA Astrophysics Data System (ADS)
Li, T.; Yeoh, L. A.; Srinavasan, A.; Klochan, O.; Ritchie, D. A.; Simmons, M. Y.; Sushkov, O. P.; Hamilton, A. R.
2016-05-01
Gauge theories, while describing fundamental interactions in nature, also emerge in a wide variety of physical systems. Abelian gauge fields have been predicted and observed in a number of novel quantum many-body systems, topological insulators, ultracold atoms, and many others. However, the non-Abelian gauge field, while playing the most fundamental role in particle physics, up to now has remained a purely theoretical construction in many-body physics. In this paper, we report an observation of a non-Abelian gauge field in a spin-orbit coupled quantum system. The gauge field manifests itself in quantum magnetic oscillations of a hole doped two-dimensional (2D) GaAs heterostructure. Transport measurements were performed in tilted magnetic fields, where the effect of the emergent non-Abelian gauge field was controlled by the components of the magnetic field in the 2D plane.
Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
NASA Astrophysics Data System (ADS)
Hu, Zi-Xiang; Lee, Ki H.; Rezayi, Edward H.; Wan, Xin; Yang, Kun
2011-03-01
We study the scaling behavior in the tunneling amplitude when quasiparticles tunnel along a straight path between the two edges of a fractional quantum Hall annulus. Such scaling behavior originates from the propagation and tunneling of charged quasielectrons and quasiholes in an effective field analysis. In the limit when the annulus deforms continuously into a quasi-one-dimensional (1D) ring, we conjecture the exact functional form of the tunneling amplitude for several cases, which reproduces the numerical results in finite systems exactly. The results for Abelian quasiparticle tunneling is consistent with the scaling analysis; this allows for the extraction of the conformal dimensions of the quasiparticles. We analyze the scaling behavior of both Abelian and non-Abelian quasiparticles in the Read-Rezayi { Z}_k -parafermion states. Interestingly, the non-Abelian quasiparticle tunneling amplitudes exhibit non-trivial k-dependent corrections to the scaling exponent.
Properties of Non-Abelian Fractional Quantum Hall States at Filling ν=k/r
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Haldane, F. D. M.
2008-12-01
We compute the physical properties of non-Abelian fractional quantum Hall (FQH) states described by Jack polynomials at general filling ν=k/r. For r=2, these states are the Zk Read-Rezayi parafermions, whereas for r>2 they represent new FQH states. The r=k+1 states, multiplied by a Vandermonde determinant, are a non-Abelian alternative construction of states at fermionic filling 2/5,3/7,4/9,…. We obtain the thermal Hall coefficient, the quantum dimensions, the electron scaling exponent, and the non-Abelian quasihole propagator. The properties of the r>2 Jack polynomials indicate they are correlators of fields of nonunitary conformal field theories (CFT), but the CFT-FQH connection fails when invoked to compute physical properties such as the quasihole propagator. The quasihole wave function, written as a coherent state representation of Jack polynomials, has an identical structure for all non-Abelian states.
Non-abelian black holes and black strings in higher dimensions
Hartmann, Betti
2009-05-01
We review the properties of static, higher dimensional black hole solutions in theories where non-abelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in d>4, but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein-Yang-Mills models. 5-dimensional black strings with horizon topology S{sup 2}xS{sup 1} are also discussed. These are so-called undeformed and deformed non-abelian black strings, which are translationally invariant and correspond to 4-dimensional non-abelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axially symmetric for constant values of the extra coordinate is a new feature as compared to black string solutions of Einstein (-Maxwell) theory. It is argued that these non-abelian black strings are thermodynamically unstable.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
Mixed symmetry Wilson-loop interactions in the worldline formalism
NASA Astrophysics Data System (ADS)
Edwards, James P.; Corradini, Olindo
2016-09-01
Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation. This work has direct application to physical observables such as scattering amplitudes in the presence of such a matter multiplet and lifts the restriction on the type of matter that has previously featured in worldline calculations.
A universal symmetry detection algorithm.
Maurer, Peter M
2015-01-01
Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
Sekhar Chivukula
2016-07-12
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was presentÂ at the classical level. Â Quantum Chromodynamics (QCD),Â the modern theoryÂ of the strong interactions, exemplify each ofÂ these possibilities.Â The interplayÂ of these effects determine theÂ spectrum of particles that we observeÂ and, ultimately, account forÂ 99% of the mass of ordinary matter.Â
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
U(1) symmetries in F-theory GUTs with multiple sections
NASA Astrophysics Data System (ADS)
Mayrhofer, Christoph; Palti, Eran; Weigand, Timo
2013-03-01
We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to a non-Abelian gauge group G. The formalism is generally applicable to models in global Tate form but we focus on the phenomenologically interesting case of G = SU(5). The Abelian gauge factors arise due to extra global sections resulting from a specific factorisation of the Tate polynomial which describes the elliptic fibration. These constructions, which accommodate up to four different U(1) factors, are worked out in detail for the two possible embeddings of a single U(1) factor into E 8, usually denoted SU(5) × U(1) X and SU(5) × U(1) PQ . The resolved models can be understood either patchwise via a small resolution or in terms of a {{{P}}_{1,1,2 }} [4] description of the elliptic fibration. We derive the U(1) charges of the fields from the geometry, construct the U(1) gauge fluxes and exemplify the structure of the Yukawa interaction points. A particularly interesting result is that the global SU(5) × U(1) PQ model exhibits extra SU(5)-singlet states which are incompatible with a single global decomposition of the 248 of E 8. The states in turn lead to new Yukawa type couplings which have not been considered in local model building.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Topological phases with generalized global symmetries
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2016-04-01
We present simple lattice realizations of symmetry-protected topological phases with q -form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d +1 ) -colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Cao Qinghong; Khalil, Shaaban; Ma, Ernest; Okada, Hiroshi
2011-10-01
We discuss how {theta}{sub 13}{ne}0 is accommodated in a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T{sub 7} in the context of a supersymmetric extension of the standard model with gauged U(1){sub B-L}. We predict a correlation between {theta}{sub 13} and {theta}{sub 23}, as well as the effective neutrino mass m{sub ee} in neutrinoless double beta decay.
Energy-momentum correlations for Abelian Higgs cosmic strings
NASA Astrophysics Data System (ADS)
Daverio, David; Hindmarsh, Mark; Kunz, Martin; Lizarraga, Joanes; Urrestilla, Jon
2016-04-01
We report on the energy-momentum correlators obtained with recent numerical simulations of the Abelian Higgs model, essential for the computation of cosmic microwave background and matter perturbations of cosmic strings. Due to significant improvements both in raw computing power and in our parallel simulation framework, the dynamical range of the simulations has increased fourfold both in space and time, and for the first time we are able to simulate strings with a constant physical width in both the radiation and matter eras. The new simulations improve the accuracy of the measurements of the correlation functions at the horizon scale and confirm the shape around the peak. The normalization is slightly higher in the high wave-number tails, due to a small increase in the string density. We study, for the first time, the behavior of the correlators across cosmological transitions and discover that the correlation functions evolve adiabatically; i.e., the network adapts quickly to changes in the expansion rate. We propose a new method for constructing source functions for Einstein-Boltzmann integrators, comparing it with two other methods previously used. The new method is more consistent, easier to implement, and significantly more accurate.
Fast non-Abelian geometric gates via transitionless quantum driving
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
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.
Fast non-Abelian geometric gates via transitionless quantum driving.
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.
Qi Ran; Liu, W. M.; Yu, Xiao-Lu; Li, Z. B.
2009-05-08
We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which contains non-Abelian Josephson effect and has very different density and spin tunneling characters compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, respectively, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.
Residual symmetries of the gravitational field
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Velázquez-Rodríguez, Gerardo
2016-02-01
We develop a geometric criterion that unambiguously characterizes the residual symmetries of a gravitational Ansatz. It also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz. We apply the criterion to several examples starting with the Collinson Ansatz for circular stationary axisymmetric spacetimes. We reproduce the residual symmetries already known for this Ansatz including their conformal symmetry, for which we identify the corresponding infinite generators spanning the two related copies of the Witt algebra. We also consider the noncircular generalization of this Ansatz and show how the noncircular contributions on the one hand break the conformal invariance and on the other hand enhance the standard translation symmetries of the circular Killing vectors to supertranslations depending on the direction along which the circularity is lost. As another application of the method, the well-known relation defining conjugate gravitational potentials introduced by Chandrasekhar, which makes possible the derivation of the Kerr black hole from a trivial solution of the Ernst equations, is deduced as a special point of the general residual symmetry of the Papapetrou Ansatz. In this derivation we emphasize how the election of Weyl coordinates, which determines the Papapetrou Ansatz, breaks also the conformal freedom of the stationary axisymmetric spacetimes. Additionally, we study AdS waves for any dimension generalizing the residual symmetries already known for lower dimensions and exhibiting a very complex infinite-dimensional Lie algebra containing three families: two of them span the semidirect sum of the Witt algebra and scalar supertranslations and the third generates vector supertranslations. Independently of this complexity we manage to comprehend the true meaning of the infinite connected group as the precise diffeomorphisms subgroup allowing to locally deform the AdS background into Ad
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. PMID:11223922
Symmetry in context: salience of mirror symmetry in natural patterns.
Cohen, Elias H; Zaidi, Qasim
2013-05-31
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.
Symmetry in context: Salience of mirror symmetry in natural patterns
Cohen, Elias H.; Zaidi, Qasim
2013-01-01
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo E-mail: luca.santoni@sns.it E-mail: filippo.vernizzi@cea.fr
2015-09-01
Effective theories of a scalar φ invariant under the internal galileon symmetry φ→φ+b{sub μ} x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would
Symmetry constraint for foreground extraction.
Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai
2014-05-01
Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.
Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels
Burrello, Michele; Trombettoni, Andrea
2011-10-15
We study ultracold atoms subjected to U(2) non-Abelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous non-Abelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spin-orbit interaction (e.g., obtained through the rotation of two-dimensional atomic gases coupled with a tripod scheme). The single-particle energy spectrum can be analytically determined for a class of gauge potentials, whose physical implementation is discussed. The corresponding Landau levels are deformed by the non-Abelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intraspecies interaction) are determined far from and at the degeneracy points of the Landau levels, where non-Abelian states appear. We present a discussion of the effect of the angular momentum, as well as results for U(3) gauge potentials.
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2011-09-01
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z4 parafermion (Read-Rezayi) state is a special case. This provides an example in which Z2 electron fractionalization leads to non-Abelian topological phases. The naive “ideal” wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
Barkeshli, Maissam; Wen Xiaogang
2011-09-15
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub orbifold FQH states, of which the Z{sub 4} parafermion (Read-Rezayi) state is a special case. This provides an example in which Z{sub 2} electron fractionalization leads to non-Abelian topological phases. The naive ''ideal'' wave functions and ideal Hamiltonians associated with these orbifold states do not in general correspond to incompressible phases but, instead, lie at a nearby critical point. We discuss this unusual situation from the perspective of the pattern-of-zeros/vertex algebra frameworks and discuss implications for the conceptual foundations of these approaches. Due to the proximity in the phase diagram of these non-Abelian states to the (ppq) bilayer states, they may be experimentally relevant, both as candidates for describing the plateaus in single-layer systems at filling fractions 8/3 and 12/5 and as a way to tune to non-Abelian states in double-layer or wide quantum wells.
Gauge U(1) dark symmetry and radiative light fermion masses
NASA Astrophysics Data System (ADS)
Kownacki, Corey; Ma, Ernest
2016-09-01
A gauge U (1) family symmetry is proposed, spanning the quarks and leptons as well as particles of the dark sector. The breaking of U (1) to Z2 divides the two sectors and generates one-loop radiative masses for the first two families of quarks and leptons, as well as all three neutrinos. We study the phenomenological implications of this new connection between family symmetry and dark matter. In particular, a scalar or pseudoscalar particle associated with this U (1) breaking may be identified with the 750 GeV diphoton resonance recently observed at the Large Hadron Collider (LHC).
Gauge Invariant U(1) Field Theories with Magnetic Monopole Symmetry.
NASA Astrophysics Data System (ADS)
Goldman, Neil
1982-03-01
A quantum field theory of a magnetically and electrically charged fermion field is developed. This is done for an abelian duet of vector boson fields in a U(1), gauge invariant manner. The U(1) symmetry is maintained through a scalar field interacting with the boson fields. The gauge invariance is preserved by extending the Mandelstam path dependent method for electromagnetism. This is done without recourse to Dirac strings or solitons. Further, the energy momentum and angular momentum tensor operators are found explicitly in terms of path dependent variables. A two dimensional charge space is coupled invariantly with the vector boson duet preserving the symmetry of the fermion monopole interactions with the use of the axial vector current, avoiding explicit use of the dual field tensor terms. It is found that if the postulated symmetries are not broken, only part of the Lorentz force law's dual tensor interaction term emerges in the low energy first order in the coupling constant limit. If the mediating scalar field is in the Higg's gauge, the following constraint is found:. 2(pi)n = SQRT.(2m(,0)(lamda)/f, where n = 0, (+OR -)1, (+OR-)2...,. and m(,0) and f are the Higg's model parameters and (lamda) is the coupling constant for the vector boson fields with the scalar fields. The Feynman diagrams are found for the Green's functions in a path dependent, gauge invariant formulation. This situation leads to a specific model for studying the scalar mediating field from a vacuum point of view, and for future work, by breaking the symmetry with the fermion field interaction.
Pauli-Villars Regularization of Non-Abelian Gauge Theories
NASA Astrophysics Data System (ADS)
Hiller, J. R.
2016-07-01
As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.
Noncommutative geometry and non-Abelian Berry phase in the wave-packet dynamics of Bloch electrons
NASA Astrophysics Data System (ADS)
Shindou, Ryuichi; Imura, Ken-Ichiro
2005-08-01
Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest in the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show, using only the fundamental principles of quantum mechanics, that the effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a non-Abelian gauge field associated with a geometric Berry phase. Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. On the other hand, the degeneracy of Bloch bands makes the gauge fields non-Abelian. For the purpose of applying our wave-packet dynamics to the analyses on transport phenomena in the context of Berry phase engineering, we focused on the Hall-type and polarization currents. Our formulation turned out to be useful for investigating and classifying various types of topological current on the same footing. We highlighted their symmetries, in particular, their behavior under time reversal ( T) and space inversion ( I). The result of these analyses was summarized as a set of cancellation rules. We also introduced the concept of parity
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures
Phuc, Nguyen Thanh; Tatara, Gen; Kawaguchi, Yuki; Ueda, Masahito
2015-01-01
Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices. PMID:26330292
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
On non-abelian T-dual geometries with Ramond fluxes
NASA Astrophysics Data System (ADS)
Sfetsos, Konstadinos; Thompson, Daniel C.
2011-05-01
We show how to implement T-duality along non-abelian isometries in backgrounds with non-vanishing Ramond fields. When the dimension of the isometry group is odd (even) the duality swaps (preserves) the chirality of the theory. In certain cases a non-abelian duality can result in a massive type-IIA background. We provide two examples by dualising SU(2) isometry subgroups in AdS×S and AdS×S×T. The resultant dual geometries inherit the original AdS factors but have transverse spaces with reduced isometry and preserve only half of the original supersymmetry. The non-abelian dual of AdS×S has an M-theory lift which is related to the gravity duals of N=2 superconformal theories. We comment on a possible interpretation of this as a high spin limit.
Question of Abelian-Higgs hair expulsion from extremal dilaton black holes
NASA Astrophysics Data System (ADS)
Moderski, Rafał; Rogatko, Marek
1999-11-01
It has been argued that the extremal dilaton black holes exhibit a flux expulsion of Abelian-Higgs vortices. We carefully reexamine the problem and give analytic proofs for the flux expulsion to always take place. We also conduct a numerical analysis of the problem using three initial data sets on the horizon of an extreme dilatonic black hole, namely, core, vacuum, and sinusoidal initial conditions. We also show that an AbelianHiggs vortex can end on the extremal dilaton black hole. Concluding, we calculate the back reaction of the Abelian-Higgs vortex on the geometry of the extremal black hole and draw a conclusion that a straight cosmic string and the extreme dilatonic black hole hardly felt their presence.
A fresh look at the flux tube in Abelian-projected SU(2) gluodynamics
NASA Astrophysics Data System (ADS)
Koma, Y.; Koma, M.; Suzuki, T.; Ilgenfritz, E.-M.; Polikarpov, M. I.
2003-05-01
We reconsider the properties of the QQ¯ flux tube within Abelian-projected SU(2) lattice gauge theory in terms of electric field and monopole current. In maximal Abelian gauge fixing, we assess the influence of Gribov copies on the apparent flux-tube profile. For the profile corresponding to optimal gauge fixing, we study the independence of the lattice spacing for β = 2.3, 2.4, and 2.5115 on a 32 4 lattice. We apply the decomposition of the Abelian Wilson loop into monopole and photon parts and compare the electric and monopole profile emerging from these three different sources with the field strength and monopole current within the DGL theory.
Permutation-symmetry related selection rules in spinor quantum gases
NASA Astrophysics Data System (ADS)
Yurovsky, Vladimir
2014-05-01
Selection rules constraining possible transitions between states of quantum systems can be derived from the system symmetry. Invariance over permutations of indistinguishable particles, contained in each physical system, is one of the basic symmetries. Consider a many-body system with separable spin and spatial degrees of freedom of particles with arbitrary spins s. Eigenfunctions of such systems can be expressed as a sum of products of spin and spatial functions, which form irreducible representations (irreps) of the symmetric group. The quantum numbers are the Young diagrams λ = [λ1 , ... ,λ2 s + 1 ] . The selection rules for a general k-body interactions allow transitions between the states λ and λ' only if ∑m=12s+1 |λm -λm'| <= 2 k . For s = 1 / 2 , the Young diagrams are unambiguously related to the total spin, and if k = 1 , we get the conventional selection rule for dipole transitions. However, if s > 1 / 2 , the rules cannot be expressed in terms of spins. The selection rules provide a way of control over the formation of many-body entangled states, belonging to multidimensional, non-Abelian irreps of the symmetric group. The effects can be observed with spinor atoms in an optical lattice in the Mott-insulator regime.
Non-vanishing U e3 under S 3 symmetry
NASA Astrophysics Data System (ADS)
Siyeon, Kim
2012-07-01
This work proposes two models of neutrino masses that predict non-zero θ 13 under the non-Abelian discrete flavor symmetry {S}3⊗{Z}2. We advocate that the size of θ 13 is understood as a group theoretical consequence rather than a perturbed effect from the tri-bi-maximal mixing. So, the difference of two models is designed only in terms of the flavor symmetry, by changing the charge assignment of right-handed neutrinos. The PMNS matrix in the first model is obtained from both mass matrices, charged leptons giving rise to non-zero θl_{13} and neutrino masses giving rise to tri-bi-maximal mixing. The physical mixing angles are expressed by a simple relation between θl_{13} and tri-bi-maximal angles to fit the recent experimental results. The other model generates PMNS matrix with non-zero θ 13, only from the neutrino mass transformation. The 5-dimensional effective theory of Majorana neutrinos obtained in this framework is tested with phenomenological bounds in the parametric spaces sin θ 23,sin θ 12 and m 2/ m 3 vs. sin θ 13.
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.
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.
Nahum, Adam; Serna, P; Chalker, J T; Ortuño, M; Somoza, A M
2015-12-31
We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.
Nahum, Adam; Serna, P; Chalker, J T; Ortuño, M; Somoza, A M
2015-12-31
We show numerically that the "deconfined" quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP(1) model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories. PMID:26765019
NASA Astrophysics Data System (ADS)
Carter, Brandon
2010-02-01
The principles of a previously developed formalism for the covariant treatment of multiscalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type—but curved—are recapitulated. Their application is extended from ordinary harmonic models to a more general category of harmonious field models, with emphasis on cases in which the field is confined to a string or higher brane world sheet, and for which the relevant internal symmetry group is non-Abelian, so that the conditions for conservation of the corresponding charge currents become rather delicate, particularly when the symmetry is gauged. Attention is also given to the conditions for conservation of currents of a different kind—representing surface fluxes of generalized momentum or energy—associated with symmetries not of the internal target space but of the underlying space-time background structure, including the metric and any relevant gauge field. For the corresponding current to be conserved the latter need not be manifestly invariant: preservation modulo a gauge adjustment will suffice. The simplest case is that of “strong” symmetry, meaning invariance under the action of an effective Lie derivative (an appropriately gauge adjusted modification of an ordinary Lie derivative). When the effective symmetry is of the more general “weak” kind, the kinetic part of the current is not conserved by itself but only after being supplemented by a suitable contribution from the background.
NASA Astrophysics Data System (ADS)
Lan, Tian; Kong, Liang; Wen, Xiao-Gang
2016-10-01
We propose a systematic framework to classify (2+1)-dimensional (2+1D) fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry G . The key is to use the so-called symmetric fusion category E to describe the symmetry. Here, E =sRep (Z2f) describing particles in a fermionic product state without symmetry, or E =sRep (Gf) [E =Rep (G )] describing particles in a fermionic (bosonic) product state with symmetry G . Then, topological orders with symmetry E are classified by nondegenerate unitary braided fusion categories over E , plus their modular extensions and total chiral central charges. This allows us to obtain a list that contains all 2+1D fermionic topological orders without symmetry. For example, we find that, up to p +i p fermionic topological orders, there are only four fermionic topological orders with one nontrivial topological excitation: (1) the K =( -1 0 0 2) fractional quantum Hall state, (2) a Fibonacci bosonic topological order stacking with a fermionic product state, (3) the time-reversal conjugate of the previous one, and (4) a fermionic topological order with chiral central charge c =1/4 , whose only topological excitation has non-Abelian statistics with spin s =1/4 and quantum dimension d =1 +√{2 } .
Quintet pairing and non-Abelian vortex string in spin- 3/2 cold atomic systems
Wu, C.
2010-03-02
We study the s-wave quintet Cooper pairing phase (S{sub pair} = 2) in spin-3/2 cold atomic systems and identify various novel features which do not appear in spin-1/2 pairing systems. A single quantum vortex is shown to be energetically less stable than a pair of half-quantum vortices. The half-quantum vortex exhibits the global analogue of the non-Abelian Alice string and SO(4) Cheshire charge in gauge theories. The non-Abelian half-quantum vortex loop enables topological generation of quantum entanglement.
Cold Atoms in Non-Abelian Gauge Potentials: From the Hofstadter Moth to Lattice Gauge Theory
Osterloh, K.; Baig, M.; Santos, L.; Zoller, P.; Lewenstein, M.
2005-07-01
We demonstrate how to create artificial external non-Abelian gauge potentials acting on cold atoms in optical lattices. The method employs atoms with k internal states, and laser assisted state sensitive tunneling, described by unitary kxk matrices. The single-particle dynamics in the case of intense U(2) vector potentials lead to a generalized Hofstadter butterfly spectrum which shows a complex mothlike structure. We discuss the possibility to realize non-Abelian interferometry (Aharonov-Bohm effect) and to study many-body dynamics of ultracold matter in external lattice gauge fields.
Generalized flux-tube solution in Abelian-projected SU(N) gauge theory
NASA Astrophysics Data System (ADS)
Koma, Yoshiaki
2002-12-01
The [U(1)]N-1 dual Ginzburg-Landau (DGL) theory as a low-energy effective theory of Abelian-projected SU(N) gauge theory is formulated in a Weyl symmetric way. The string tensions of the flux-tube solutions of the DGL theory associated with color-electric charges in various representations of SU(N) are calculated analytically at the border between type I and type II of the dual superconducting vacuum (Bogomol’nyi limit). The resulting string tensions satisfy the flux counting rule, which reflects the non-Abelian nature of gauge theory.
Necessity of an energy barrier for self-correction of Abelian quantum doubles
NASA Astrophysics Data System (ADS)
Kómár, Anna; Landon-Cardinal, Olivier; Temme, Kristan
2016-05-01
We rigorously establish an Arrhenius law for the mixing time of quantum doubles based on any Abelian group Zd. We have made the concept of the energy barrier therein mathematically well defined; it is related to the minimum energy cost the environment has to provide to the system in order to produce a generalized Pauli error, maximized for any generalized Pauli errors, not only logical operators. We evaluate this generalized energy barrier in Abelian quantum double models and find it to be a constant independent of system size. Thus, we rule out the possibility of entropic protection for this broad group of models.
Conformal flatness, non-Abelian Kaluza-Klein reduction and quaternions
NASA Astrophysics Data System (ADS)
Maraner, Paolo; Pachos, Jiannis K.
2012-02-01
The non-Abelian Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions and signatures. The corresponding equations are particularly elegant when the internal space supports a global Killing parallelization. Assuming this imposes the generalized 'spacetime' to be maximally symmetric with holonomy in the unitary quaternionic group Sp(d/4). Recalling an analogous result for the complex case, we conclude that all special manifolds with constant properly 'holonomy-related' sectional curvature, are in natural correspondence with conformally flat, possibly non-Abelian, Kaluza-Klein spaces.
Non-Abelian geometric phase and long-range atomic forces
NASA Technical Reports Server (NTRS)
Zygelman, B.
1990-01-01
It is shown how gauge fields, or geometric phases, manifest as observable effects in both bound and free diatom systems. It is shown that, in addition to altering energy splittings in bound systems, geometric phases induce transitions in levels separated by a finite-energy gap. An example is given where the non-Abelian gauge field couples nondegenerate electronic levels in a diatom. This gauge-field coupling gives rise to an observable effect. It is shown that when the diatom is 'pulled apart', the non-Abelian geometric phase manifests as a long-range atomic force.
Reflections on Symmetry and Proof
ERIC Educational Resources Information Center
Merrotsy, Peter
2008-01-01
The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…
Dynamical Symmetries in Classical Mechanics
ERIC Educational Resources Information Center
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
-session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: · Quesne C 2013, J. Math. Phys. 54, 102102. · Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) · Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard Berssenbrügge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing
Hexagonal projected symmetries.
Oliveira, Juliane F; Castro, Sofia B S D; Labouriau, Isabel S
2015-09-01
In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern. PMID:26317198
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Chiral symmetry and pentaquarks
Dmitri Diakonov
2004-07-01
Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.
From non-Abelian anyons to quantum computation to coin-flipping by telephone
NASA Astrophysics Data System (ADS)
Mochon, Carlos
Following their divorce, Alice and Bob would like to split some of their possessions by flipping a coin. Unwilling to meet in person, and without a trusted third party, they must figure out a scheme to flip the coin over a telephone that guarantees that neither party can cheat. The preceding scenario is the traditional definition of two-party coin-flipping. In a classical setting, without limits on the available computational power, one player can always guarantee a coin-flipping victory by cheating. However, by employing quantum communication it is possible to guarantee, with only information-theoretic assumptions, that neither party can win by cheating, with a probability greater than two thirds. Along with the description of such a protocol, this thesis derives a tight lower bound on the bias for a large family of quantum weak coin-flipping protocols, proving such a protocol optimal within the family. The protocol described herein is an improvement and generalization of one examined by Spekkens and Rudolph. The key steps of the analysis involve Kitaev's description of quantum coin-flipping as a semidefinite program whose dual problem provides a certificate that upper bounds the amount of cheating for each party. In order for such quantum protocols to be viable, though, a number of practical obstacles involving the communication and processing of quantum information must be resolved. In the second half of this thesis, a scheme for processing quantum information is presented, which uses non-abelian anyons that are the magnetic and electric excitations of a discrete-group quantum gauge theory. In particular, the connections between group structure and computational power are examined, generalizing previous work by Kitaev, Ogburn and Preskill. Anyon based computation has the advantage of being topological, which exponentially suppresses the rate of decoherence and the errors associated with the elementary quantum gates. Though no physical systems with such
NASA Astrophysics Data System (ADS)
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
Symmetries in laminated composite plates
NASA Technical Reports Server (NTRS)
Noor, A. K.
1976-01-01
The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.
Symmetry in DIET phase transitions
NASA Astrophysics Data System (ADS)
Zhang, J. P.; Marks, L. D.
1989-11-01
Analysis of the route of the phase transitions in transition metal oxides driven by DIET of oxygen from the surfaces observed by high resolution electron microscopy indicates that there is a symmetry selection rule. The phase transitions are to a structure with a higher point group symmetry where the new phase with a lower oxygen content is either one with a supergroup symmetry with respect to the original phase, or is an amorphous intermediary. The final phase has the highest symmetry and is also a metallic conductor. If a possible lower oxygen content phase does not have the correct supergroup symmetry, it is not formed. It is also found that the point group is conserved during the phase transition if the oxide belongs to the highest groups O h or D 6h. This symmetry selection rule can therefore be used to predict the route of the phase transition. The symmetry rule operates when the phase transition is diffusional.
NASA Astrophysics Data System (ADS)
Iyer, B. R.; Kamran, N.
1991-09-01
The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.
Monopoles in non-Abelian Born-Infeld-Higgs theory and Born-Infeld collapse
NASA Astrophysics Data System (ADS)
Dyadichev, V. V.; Gal'Tsov, D. V.
2002-06-01
Regular magnetic monopoles in the non-Abelian Born-Infeld-Higgs theory are known to exist in the region of the field strength parameter β>βcr, bounded from below. Beyond this region, only pointlike (embedded Abelian) monopoles exist, and we show that the transition from the regular to singular structure is reminiscent of gravitational collapse. Near the threshold behavior is characterized by the rapidly increasing negative pressure, which typically arises in the high density non-Abelian Born-Infeld (NBI) matter. Another feature, shared by both the NBI and gravitating monopoles, is the existence of excited states, which can be thought of as bound states of monopoles and sphalerons. These are labeled by the number N of nodes of the Yang-Mills function. Their masses are greater than the mass of the ground state monopole, and they are expected to be unstable. The sequence of masses MN rapidly converges to the mass of the embedded Abelian solution with a constant Higgs boson. The ratio of the sphaleron size to that of the monopole grows with decreasing β, and, at the same time, both fall down until the solutions cease to exist, again exhibiting a collapse to the point-like monopole. The results are presented and compared both for the ordinary and the symmetrized trace NBI actions.
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.
A Note on the Abelian Sandpile in ±b{{Z}}d
NASA Astrophysics Data System (ADS)
Tyomkyn, Mykhaylo
2012-09-01
We analyze the abelian sandpile model on ℤ d for the starting configuration of n particles in the origin and 2 d-2 particles otherwise. We give a new short proof of the theorem of Fey, Levine and Peres (J. Stat. Phys. 198:143-159, 2010) that the radius of the toppled cluster of this configuration is O( n 1/ d ).
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.
Symmetry-breaking boundary states for WZW models
NASA Astrophysics Data System (ADS)
Blakeley, Daniel; Recknagel, Andreas
2009-01-01
Starting with the SU(2 WZW model, we construct boundary states that generically preserve only a parafermion times Virasoro subalgebra of the full affine Lie algebra symmetry of the bulk model. The boundary states come in families: intervals for generic k, quotients of SU(2) by discrete groups if k is a square. In that case, special members of the families can be viewed as superpositions of rotated Cardy branes. Using embeddings of SU(2) into higher groups, the new boundary states can be lifted to symmetry-breaking branes for other WZW models.
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
Non-Abelian duality and confinement: From N=2 to N=1 supersymmetric QCD
Shifman, M.; Yung, A.
2011-05-15
Recently, we discovered and discussed non-Abelian duality in the quark vacua of N=2 super-Yang-Mills theory with the U(N) gauge group and N{sub f} flavors (N{sub f}>N). Both theories from the dual pair support non-Abelian strings, which confine monopoles. Now we introduce an N=2-breaking deformation, a mass term {mu}A{sup 2} for the adjoint fields. Starting from a small deformation, we eventually make it large, which enforces complete decoupling of the adjoint fields. We show that the above non-Abelian duality fully survives in the limit of N=1 supersymmetric QCD (SQCD), albeit some technicalities change. For instance, non-Abelian strings which used to be Bogomol'nyi-Prasad-Sommerfield saturated in the N=2 limit, cease to be saturated in N=1 SQCD. Our duality is a distant relative of Seiberg's duality in N=1 SQCD. Both share some common features, but have many drastic distinctions. This is due to the fact that Seiberg's duality apply to the monopole rather than quark vacua. More specifically, in our theory we deal with N
Non-abelian gauge extensions for B-decay anomalies
NASA Astrophysics Data System (ADS)
Boucenna, Sofiane M.; Celis, Alejandro; Fuentes-Martín, Javier; Vicente, Avelino; Virto, Javier
2016-09-01
We study the generic features of minimal gauge extensions of the Standard Model in view of recent hints of lepton-flavor non-universality in semi-leptonic b → sℓ+ℓ- and b → cℓν decays. We classify the possible models according to the symmetry-breaking pattern and the source of flavor non-universality. We find that in viable models the SU (2) L factor is embedded non-trivially in the extended gauge group, and that gauge couplings should be universal, hinting to the presence of new degrees of freedom sourcing non-universality. Finally, we provide an explicit model that can explain the B-decay anomalies in a coherent way and confront it with the relevant phenomenological constraints.
NASA Astrophysics Data System (ADS)
Strocchi, Franco
One of the most powerful ideas of modern theoretical physics is the mechanism of spontaneous symmetry breaking. It is at the basis of most of the recent achievements in the description of phase transitions in Statistical Mechanics as well as of collective phenomena in solid state physics. It has also made possible the unification of weak, electromagnetic and strong interactions in elementary particle physics. Philosophically, the idea is very deep and subtle (this is probably why its exploitation is a rather recent achievement) and the popular accounts do not fully do justice to it.
NASA Astrophysics Data System (ADS)
Houtz, Rachel; Colwell, Kitran; Terning, John
2016-09-01
We explore a new class of natural models which ensure the one-loop divergences in the Higgs mass are cancelled. The top-partners that cancel the top loop are new gauge bosons, and the symmetry relation that ensures the cancellation arises at an infrared fixed point. Such a cancellation mechanism can, a la Little Higgs models, push the scale of new physics that completely solves the hierarchy problem up to 5-10 TeV. When embedded in a supersymmetric model, the stop and gaugino masses provide the cutoffs for the loops, and the mechanism ensures a cancellation between the stop and gaugino mass dependence of the Higgs mass parameter.
Non-Abelian dark matter: Models and constraints
NASA Astrophysics Data System (ADS)
Chen, Fang; Cline, James M.; Frey, Andrew R.
2009-10-01
Numerous experimental anomalies hint at the existence of a dark matter (DM) multiplet χi with small mass splittings. We survey the simplest such models which arise from DM in the low representations of a new SU(2) gauge symmetry, whose gauge bosons have a small mass μ≲1GeV. We identify preferred parameters Mχ≅1TeV, μ˜100MeV, αg˜0.04, and the χχ→4e annihilation channel, for explaining PAMELA, Fermi, and INTEGRAL/SPI lepton excesses, while remaining consistent with constraints from relic density, diffuse gamma rays, and the CMB. This consistency is strengthened if DM annihilations occur mainly in subhalos, while excitations (relevant to the excited DM proposal to explain the 511 keV excess) occur in the galactic center, due to higher velocity dispersions in the galactic center, induced by baryons. We derive new constraints and predictions which are generic to these models. Notably, decays of excited DM states χ'→χγ arise at one loop and could provide a new signal for INTEGRAL/SPI; big bang nucleosynthesis constraints on the density of dark SU(2) gauge bosons imply a lower bound on the mixing parameter γ between the SU(2) gauge bosons and photon. These considerations rule out the possibility of the gauge bosons that decay into e+e- being long-lived. We study in detail models of doublet, triplet, and quintuplet DM, showing that both normal and inverted mass hierarchies can occur, with mass splittings that can be parametrically smaller [e.g., O(100)keV] than the generic MeV scale of splittings. A systematic treatment of Z2 symmetry, which insures the stability of the intermediate DM state, is given for cases with inverted mass hierarchy, of interest for boosting the 511 keV signal from the excited dark matter mechanism.
NASA Technical Reports Server (NTRS)
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro
2010-01-01
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of “rank two” can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
Tsurumaru, Toyohiro
2010-01-15
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C{sub 4}, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of 'rank two' can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
Classical dynamics of the Abelian Higgs model from the critical point and beyond
NASA Astrophysics Data System (ADS)
Katsimiga, G. C.; Diakonos, F. K.; Maintas, X. N.
2015-09-01
We present two different families of solutions of the U(1)-Higgs model in a (1 + 1) dimensional setting leading to a localization of the gauge field. First we consider a uniform background (the usual vacuum), which corresponds to the fully higgsed-superconducting phase. Then we study the case of a non-uniform background in the form of a domain wall which could be relevantly close to the critical point of the associated spontaneous symmetry breaking. For both cases we obtain approximate analytical nodeless and nodal solutions for the gauge field resulting as bound states of an effective Pöschl-Teller potential created by the scalar field. The two scenaria differ only in the scale of the characteristic localization length. Numerical simulations confirm the validity of the obtained analytical solutions. Additionally we demonstrate how a kink may be used as a mediator driving the dynamics from the critical point and beyond.
Twofold PT symmetry in doubly exponential optical lattices
NASA Astrophysics Data System (ADS)
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-01-01
We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of PT symmetry is not around zero and the potential satisfies a shifted PT -symmetry relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted PT -symmetric relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.
Dynamical Symmetries in atomic nuclei
Jolie, J.
2010-04-26
We review the use of dynamical symmetries and supersymmetries in nuclear physics using the interacting boson approximation. Special emphasis will be put on the experimental techniques used and the influence of symmetry on experimental observables. We illustrate this by a detailed study on mixed symmetry states in {sup 94}Mo. We present also experiments performed to test predictions of dynamical supersymmetries in the Pt-Au region.
Wilczek, Frank
2005-01-20
Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).
Lo, Pok Man; Swanson, Eric S.
2011-03-15
Schwinger-Dyson equations are used to study spontaneous chiral and parity symmetry breaking of three-dimensional quantum electrodynamics with two-component fermions. This theory admits a topological photon mass that explicitly breaks parity symmetry and generates a fermion mass. We show for the first time that it is possible to spontaneously break both parity and chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavors in our truncation scheme. Finally, the Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Unified Symmetry of Hamilton Systems
NASA Astrophysics Data System (ADS)
Xu, Xue-Jun; Qin, Mao-Chang; Mei, Feng-Xiang
2005-11-01
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results. The project supported by National Natural Science Foundation of China under Grant No. 10272021 and the Doctoral Program Foundation of Institution of Higher Education of China under Grant No. 20040007022
Givental Graphs and Inversion Symmetry
NASA Astrophysics Data System (ADS)
Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek
2013-05-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Control of tripod-scheme cold-atom wavepackets by manipulating a non-Abelian vector potential
Zhang Qi; Gong Jiangbin; Oh, C.H.
2010-06-15
Tripod-scheme cold atoms interacting with laser beams have attracted considerable interest for their role in synthesizing effective non-Abelian vector potentials. Such effective vector potentials can be exploited to realize an all-optical imprinting of geometric phases onto matter waves. By working on carefully designed extensions of our previous work, we show that coherent lattice structure of cold-atom sub-wavepackets can be formed and that the non-Abelian Aharonov-Bohm effect can be easily manifested via the translational motion of cold atoms. We also show that by changing the frame of reference, effects due to a non-Abelian vector potential may be connected with a simple dynamical phase effect, and that under certain conditions it can be understood as an Abelian geometric phase in a different frame of reference. Results should help design better schemes for the control of cold-atom matter waves.
The existence of self-dual vortices in a non-Abelian {Phi}{sup 2} Chern-Simons theory
Chen Shouxin; Wang Ying
2010-09-15
Applying the dynamic shooting method, we proved the existence of nontopological radially symmetric n-vortex solutions to the self-dual equation in non-Abelian Chern-Simons gauge theory with a {Phi}{sup 2}-type potential. Moreover, we obtained all possible radially symmetric nontopological bare (or 0-vortex) solutions in the non-Abelian Chern-Simons model. Meanwhile, we established the asymptotic behavior for the solutions as |x|{yields}{infinity}.
The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links
NASA Astrophysics Data System (ADS)
Carillo, Sandra; Fuchssteiner, Benno
1989-07-01
Explicit computation for a Kawamoto-type equation shows that there is a rich associated symmetry structure for four separate hierarchies of nonlinear integrodifferential equations. Contrary to the general belief that symmetry groups for nonlinear evolution equations in 1+1 dimensions have to be Abelian, it is shown that, in this case, the symmetry group is noncommutative. Its semisimple part is isomorphic to the affine Lie algebra A(1)1 associated to sl(2,C). In two of the additional hierarchies that were found, an explicit dependence of the independent variable occurs. Surprisingly, the generic invariance for the Kawamoto-type equation obtained in Rogers and Carillo [Phys. Scr. 36, 865 (1987)] via a reciprocal link to the Möbius invariance of the singularity equation of the Kaup-Kupershmidt (KK) equation only holds for one of the additional hierarchies of symmetry groups. Thus the generic invariance is not a universal property for the complete symmetry group of equations obtained by reciprocal links. In addition to these results, the bi-Hamiltonian formulation of the hierarchy is given. A direct Bäcklund transformation between the (KK) hierarchy and the hierarchy of singularity equation for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation is exhibited: This shows that the abundant symmetry structure found for the Kawamoto equation must exist for all fifth-order equations, which are known to be completely integrable since these equations are connected either by Bäcklund transformations or reciprocal links. It is shown that similar results must hold for all hierarchies emerging out of singularity hierarchies via reciprocal links. Furthermore, general aspects of the results are discussed.
Colorful Horizons with Charge in Anti-de Sitter Space
Gubser, Steven S.
2008-11-07
An Abelian gauge symmetry can be spontaneously broken near a black hole horizon in anti-de Sitter space using a condensate of non-Abelian gauge fields. A second order phase transition is shown to separate Reissner-Nordstroem-anti-de Sitter solutions from a family of symmetry-breaking solutions which preserve a diagonal combination of gauge invariance and spatial rotational invariance.
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
Particle coupled to a heat bath in non-Abelian gauge potentials
NASA Astrophysics Data System (ADS)
Guingarey, Issoufou; Avossevou, Gabriel Y. H.
2015-12-01
We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a U(2 ) gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space.
Particle coupled to a heat bath in non-Abelian gauge potentials.
Guingarey, Issoufou; Avossevou, Gabriel Y H
2015-12-01
We derive the quantum Langevin equation (QLE) for a harmonically single trapped cold atom subjected to artificial non-Abelian gauge potentials and linearly coupled to a heat bath. The independent-oscillator (IO) and the momentum-momenta coupling models are studied. In each case, the non-Abelian effect on the QLE is pointed out for a U(2) gauge transformation. For the IO model, only the generalized Lorentz force is modified by the appearance of an additive term. For the momentum-momenta coupling model, the generalized Lorentz force as well as the friction force are subjected to modifications. The dependence of the system on the magnetic field is explicit even if the gauge potential is uniform in space. PMID:26764665
Dynamical disentanglement across a point contact in a non-Abelian quantum Hall state.
Fendley, Paul; Fisher, Matthew P A; Nayak, Chetan
2006-07-21
We analyze the tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at the Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. By bosonizing the edge theory, we show that an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with the 4-terminal Rxx approximately T(-3/2), to the low-temperature limit, with Rxx(-1/10)(h/e2) approximately-T4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy loss of ln(2[square root of 2) in this crossover.
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-19
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3. PMID:21231341
Non-Abelian coset string backgrounds from asymptotic and initial data
NASA Astrophysics Data System (ADS)
Petropoulos, P. Marios; Sfetsos, Konstadinos
2007-04-01
We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space-time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are identified with the ``boundary'' backgrounds of the next member. We explicitly demonstrate that this property holds to all orders in α' for the three- and four-dimensional cosets, while the general structure of the backgrounds at hand suggests that the property holds in any dimension. The affiliation of the ``boundary'' theory to the ``bulk'' theory exhibits marginal operators, generically build on non-Abelian parafermion bilinears, dressed with a dilaton vertex operator. The dilaton is supported by the extra radial dimension, whose asymptotic value defines the boundary. Depending on the hierarchy, this boundary can be time-like or space-like with, in the latter case, potential cosmological applications.
NASA Astrophysics Data System (ADS)
Barkeshli, Maissam; Wen, Xiao-Gang
2010-11-01
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3.
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Holographic phase transitions from higgsed, non abelian charged black holes
NASA Astrophysics Data System (ADS)
Giordano, Gastón L.; Lugo, Adrián R.
2015-07-01
We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions that represent asymptotic anti-de Sitter charged black holes with partial/full gauge symme-try breaking. We then apply the AdS/CFT correspondence to study the strong coupling regime of a 2 + 1 quantum field theory at temperature T and finite chemical potential, which undergoes transitions to phases exhibiting the condensation of a composite charged vector operator below a critical temperature T c , presumably describing p + ip/p-wave su-perconductors. In the case of p + ip-wave superconductors the transitions are always of second order. But for p-wave superconductors we determine the existence of a critical value αc of the gravitational coupling (for fixed Higgs v.e.v. parameter ) beyond which the transitions become of first order. As a by-product, we show that the p-wave phase is energetically favored over the p + ip one, for any values of the parameters. We also find the ground state solutions corresponding to zero temperature. Such states are described by domain wall geometries that interpolate between AdS 4 spaces with different light veloc-ities, and for a given , they exist below a critical value of the coupling. The behavior of the order parameter as function of the gravitational coupling near the critical coupling suggests the presence of second order quantum phase transitions. We finally study the dependence of the solution on the Higgs coupling, and find the existence of a critical value beyond which no condensed solution is present.
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
-session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: · Quesne C 2013, J. Math. Phys. 54, 102102. · Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) · Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard Berssenbrügge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing
Gauge equivalence of two different IAnsaaumlItze Rfor non-Abelian charged vortices
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.
The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices
NASA Astrophysics Data System (ADS)
Benjumea, J. C.; Núñez, J.; Tenorio, Á. F.
2007-09-01
We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra mathfrak{g}_n of n×n strictly upper triangular matrices, where n ∈ ℕ {1}. We do this by proving a conjecture, which we previously advanced, about this dimension. We introduce an algorithm and use it first to study the two simplest particular cases and then to study the general case.
Towards the String representation of the dual Abelian Higgs model beyond the London limit
NASA Astrophysics Data System (ADS)
Koma, Yoshiaki; Koma (Takayama, Miho; Ebert, Dietmar; Toki, Hiroshi
2002-08-01
We perform a path-integral analysis of the string representation of the dual abelian Higgs (DAH) model beyond the London limit, where the string describing the vortex of a flux tube has a finite thickness. We show that besides an additional vortex core contribution to the string tension, a modified Yukawa interaction appears as a boundary contribution in the type-II dual superconducting vacuum. In the London limit, the modified Yukawa interaction is reduced to the Yukawa one.
Computer-assisted techniques for the verification of the Chebyshev property of Abelian integrals
NASA Astrophysics Data System (ADS)
Figueras, Jordi-Lluís; Tucker, Warwick; Villadelprat, Jordi
We develop techniques for the verification of the Chebyshev property of Abelian integrals. These techniques are a combination of theoretical results, analysis of asymptotic behavior of Wronskians, and rigorous computations based on interval arithmetic. We apply this approach to tackle a conjecture formulated by Dumortier and Roussarie in [F. Dumortier, R. Roussarie, Birth of canard cycles, Discrete Contin. Dyn. Syst. 2 (2009) 723-781], which we are able to prove for q≤2.
PREFACE: Symmetries and Integrability of Difference Equations
NASA Astrophysics Data System (ADS)
Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane
2007-10-01
The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of
Current-Current Interactions, Dynamical Symmetry - and Quantum Chromodynamics.
NASA Astrophysics Data System (ADS)
Neuenschwander, Dwight Edward, Jr.
Quantum Chromodynamics with massive gluons (gluon mass (TBOND) xm(,p)) in a contact-interaction limit called CQCD (strong coupling g (--->) (INFIN); x (--->) (INFIN)), despite its non-renormalizability and lack of hope of confinement, is nevertheless interesting for at least two reasons. (1) Some authors have suggested a relation between 4-Fermi and Yang-Mills theories. If g/x('2) << 1, then CQCD is not merely a 4-Fermi interaction, but includes 4, 6, 8, ...-Fermi non-Abelian contact interactions. (2) With the possibility of infrared slavery, perturbative evaluation of QCD in the infrared is a dubious practice. However, if g('2)/x('2) << 1 in CQCD, then the simplest 4-Fermi interaction is dominant, and CQCD admits perturbative treatment, but only in the infrared. With the dominant interaction, a dynamical Nambu-Goldstone realization of chiral symmetry -breaking (XSB) is found. Although in QCD the relation between confinement and XSB is controversial, XSB occurs in CQCD provided confinement is sacrificed.
Partial restoration of chiral symmetry in a confining string
Kharzeev, Dmitri E.; Loshaj, F.
2014-08-01
Here, we attempt to describe the interplay of confinement and chiral symmetry breaking in QCD by using the string model. We argue that in the quasi-Abelian picture of confinement based on the condensation of magnetic monopoles and the dual Meissner effect, the world sheet dynamics of the confining string can be effectively described by the 1+1 dimensional massless electrodynamics, which is exactly soluble. The transverse plane distribution of the chromoelectric field stretched between the quark and antiquark sources can then be attributed to the fluctuations in the position of the string. The dependence of the chiral condensate in the string on the (chromo-)electric field can be evaluated analytically, and is determined by the chiral anomaly and the θ-vacuum structure. Moreover, our picture allows us to predict the distribution of the chiral condensate in the plane transverse to the axis connecting the quark and antiquark. This prediction is compared to the lattice QCD results; a good agreement is found.
Non-Abelian black holes in D=5 maximal gauged supergravity
Cvetic, M.; Lue, H.; Pope, C. N.
2010-02-15
We investigate static non-Abelian black hole solutions of anti-de Sitter (AdS) Einstein-Yang-Mills-dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-Abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS{sub 2}xS{sup 3}. If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-Abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalized to dimensions other than five.
Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states
Bonderson, Parsa; Gurarie, Victor; Nayak, Chetan
2011-02-15
We study the non-Abelian statistics of quasiparticles in the Ising-type quantum Hall states which are likely candidates to explain the observed Hall conductivity plateaus in the second Landau level, most notably the one at filling fraction {nu}=5/2. We complete the program started in V. Gurarie and C. Nayak, [Nucl. Phys. B 506, 685 (1997)]. and show that the degenerate four-quasihole and six-quasihole wave functions of the Moore-Read Pfaffian state are orthogonal with equal constant norms in the basis given by conformal blocks in a c=1+(1/2) conformal field theory. As a consequence, this proves that the non-Abelian statistics of the excitations in this state are given by the explicit analytic continuation of these wave functions. Our proof is based on a plasma analogy derived from the Coulomb gas construction of Ising model correlation functions involving both order and (at most two) disorder operators. We show how this computation also determines the non-Abelian statistics of collections of more than six quasiholes and give an explicit expression for the corresponding conformal block-derived wave functions for an arbitrary number of quasiholes. Our method also applies to the anti-Pfaffian wave function and to Bonderson-Slingerland hierarchy states constructed over the Moore-Read and anti-Pfaffian states.
NASA Astrophysics Data System (ADS)
Gu, Zheng-Cheng; Wang, Juven C.; Wen, Xiao-Gang
2016-03-01
Quantum disordering a discrete-symmetry-breaking state by condensing domain walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a one-dimensional representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain walls can lead to a nontrivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a nontrivial SPT invariant, the symmetry-twist-dependent partition function. We propose two different kinds of field theories that can describe the above-mentioned SPT states. The first one is a Ginzburg-Landau-type nonlinear sigma model theory, but with an additional multikink domain-wall topological term. Such theory has an anomalous Uk(1 ) symmetry but an anomaly-free ZNk symmetry. The second one is a gauge theory, which is beyond Abelian Chern-Simons/BF gauge theories. We argue that the two field theories are equivalent at low energies. After coupling to the symmetry twists, both theories produce the desired SPT invariant.
Symmetry of charge order in cuprates.
Comin, R; Sutarto, R; He, F; da Silva Neto, E H; Chauviere, L; Fraño, A; Liang, R; Hardy, W N; Bonn, D A; Yoshida, Y; Eisaki, H; Achkar, A J; Hawthorn, D G; Keimer, B; Sawatzky, G A; Damascelli, A
2015-08-01
Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity. PMID:26006005
Functional Symmetry of Endomembranes
2007-01-01
In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation. PMID:17267686
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Symmetries in the Schwarzschild Problem
NASA Astrophysics Data System (ADS)
Mioc, V.
The two-body problem associated to a force field described by a potential of the form U = A/r + B/r3 (r is a distance between particles, A and B are real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form isomorphic commutative groups endowed with an idempotent structure. Expressed in Levi-Civita's coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting an idempotent structure.
NASA Astrophysics Data System (ADS)
Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.
2016-06-01
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.
Anatomy of a deformed symmetry: Field quantization on curved momentum space
Arzano, Michele
2011-01-15
In certain scenarios of deformed relativistic symmetries relevant for noncommutative field theories particles exhibit a momentum space described by a non-Abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group-valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of {kappa}-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for {kappa}-quantum fields.
The chiral magnetic effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory
Braguta, V. V.; Buividovich, P. V. Kalaydzhyan, T. Kuznetsov, S. V. Polikarpov, M. I.
2012-04-15
We study some properties of the non-Abelian vacuum induced by strong external magnetic field. We perform calculations in the quenched SU(3) lattice gauge theory with tadpole-improved Luescher-Weisz action and chirally invariant lattice Dirac operator. The following results are obtained: The chiral symmetry breaking is enhanced by the magnetic field. The chiral condensate depends on the strength of the applied field as a power function with exponent {nu} = 1.6 {+-} 0.2. There is a paramagnetic polarization of the vacuum. The corresponding susceptibility and other magnetic properties are calculated and compared with the theoretical estimations. There are nonzero local fluctuations of the chirality and electromagnetic current, which grow with the magnetic field strength. These fluctuations can be a manifestation of the Chiral Magnetic Effect.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
also included in these Proceedings. It was especially rewarding and greatly appreciated that symposium-founder Bruno Gruber attended all the sessions and that Dr. Hubert Regner, a distinguished official of the provincial administration and ardent supporter of the symposia for over twenty years, honoured us with a visit and an encouraging address to the participants. We wish to express our sincere gratitude to the local community, particularly the Schenk Family and the staff of Collegium Mehrerau for the selfless friendship, generosity and kind hospitality they offered our gathering. It made a lasting impression on participants and guests alike and provided an excellent basis for fruitful scientific discussions and personal interactions. This and the positive resonance from participants have encouraged us to take the experiment a step further to "Symmetries in Science 2011"! Thanks also to Yvette for continuous and reliable support. The conference and proceedings would probably not have materialized without her. Frankfurt am Main and Graz, June 2010 Dieter Schuch Michael Ramek Conference photograph
Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
NASA Astrophysics Data System (ADS)
Cartas-Fuentevilla, R.; Meza-Aldama, O.
2016-02-01
Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hypercomplex formulation of Abelian gauge field theories by incorporating a new complex unit to the usual complex one. The hypercomplex version of the traditional Mexican hat potential associated with the U(1) gauge field theory, corresponds to a hybrid potential with two real components, and with U(1)× SO(1,1) as symmetry group. Each component corresponds to a deformation of the hat potential, with the appearance of a new degenerate vacuum. Hypercomplex electrodynamics will show novel properties, such as spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and such as Aharonov-Bohm type strings defects as exact solutions; these topological defects may be detected only by quantum interference of charged particles through gauge invariant loop integrals. In a particular limit, the hyperbolic electrodynamics does not admit topological defects associated with continuous symmetries.
3d {N} = 2 mirror symmetry, pq-webs and monopole superpotentials
NASA Astrophysics Data System (ADS)
Benvenuti, Sergio; Pasquetti, Sara
2016-08-01
D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3 d {N} = 2 theories. For generic pq-webs however the low energy field theory is not known. We use 3d mirror symmetry and Type IIB S-duality to construct Abelian gauge theories corresponding to D3 branes ending on both sides of a pq-web made of many coincident N S5's intersecting one D5. These theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. In the special case of the pq-web with one D5 and one N S5, the 3d low energy SCFT admits three dual formulations. This triality can be applied locally inside bigger quiver gauge theories. We prove our statements using partial mirror symmetry à la Kapustin-Strassler, showing the equality of the S b 3 partition functions and studying the quantum chiral rings.
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Symmetry in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.
1993-01-01
Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is
NASA Astrophysics Data System (ADS)
Huang, Ching-Yu; Wei, Tzu-Chieh
2016-04-01
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular S and T matrices to study transitions in a few families of two-dimensional (2D) wave functions which are ZN (N =2 and3 ) symmetric. We find that in addition to the topologically ordered phases, the modular matrices can be used to identify nontrivial SPT phases and detect transitions between different SPT phases as well as between symmetric and symmetry-breaking phases. Therefore modular matrices can be used to characterize various types of gapped phases in a unifying way.
Novel symmetries in Christ-Lee model
NASA Astrophysics Data System (ADS)
Kumar, R.; Shukla, A.
2016-07-01
We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.
Understanding the physics of a possible non-Abelian fractional quantum hall effect state.
Pan, Wei; Crawford, Matthew; Tallakulam, Madhu; Ross, Anthony Joseph, III
2010-10-01
We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling {nu} = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at {nu} = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.
Effective models of doped quantum ladders of non-Abelian anyons
NASA Astrophysics Data System (ADS)
Soni, Medha; Troyer, Matthias; Poilblanc, Didier
2016-01-01
Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study t -J models of SU (2 ) spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by SU (2) 3 theories, which are quantum deformations of the SU (2 ) algebra. Inspired by the physics of SU (2 ) spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) t -J models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by t -J (or modified t -J -V ) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of t -J chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy τ 's and light τ 's. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light τ 's. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
A simple model for the evolution of a non-Abelian cosmic string network
NASA Astrophysics Data System (ADS)
Cella, G.; Pieroni, M.
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 argument to justify the lack of scaling for the residual cases.
Phase structure, magnetic monopoles, and vortices in the lattice Abelian Higgs model
Ranft, J.; Kripfganz, J.; Ranft, G.
1983-07-15
We present Monte Carlo calculations of lattice Abelian Higgs models in four dimensions and with charges of the Higgs particles equal to q = 1, 2, and 6. The phase transitions are studied in the plane of the two coupling constants considering separately average plaquette and average link expectation values. The density of topological excitations is studied. In the confinement phase we find finite densities of magnetic-monopole currents, electric currents, and vortex currents. The magnetic-monopole currents vanish exponentially in the Coulomb phase. The density of electric currents and vortex currents is finite in the Coulomb phase and vanishes exponentially in the Higgs phase.
Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions
Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; Biro, Tamas S.
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, v$M\\atop{n}$ {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_{T}η). 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.
Non-Abelian Bremsstrahlung and Azimuthal Asymmetries in High Energy p+A Reactions
Gyulassy, Miklos; Vitev, Ivan Mateev; Levai, Peter; Biro, Tamas S.
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 vn 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 vn without invoking kT factorization. A test of CSA mechanism is the predicted nearly linear η rapidity dependence of the vn(kTη). 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 vn(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 vn in p(D) + A and non-central A + A at same dN=dη multiplicity as observed at RHIC and LHC.« less
Probing Non-Abelian Statistics of Majorana Fermions in Ultracold Atomic Superfluid
Zhu Shiliang; Shao, L.-B.; Wang, Z. D.; Duan, L.-M.
2011-03-11
We propose an experiment to directly probe the non-Abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
Bernevig, B Andrei; Haldane, F D M
2009-02-13
We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Z_{k} parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons. PMID:19257618
NASA Astrophysics Data System (ADS)
Bernevig, B. Andrei; Haldane, F. D. M.
2009-02-01
We present model wave functions for quasielectron (as opposed to quasihole) excitations of the unitary Zk parafermion sequence (Laughlin, Moore-Read, or Read-Rezayi) of fractional quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of k+2 electrons is put together or when two clusters of k+1 electrons are formed at different positions. For Abelian fractional quantum Hall states (k=1), our construction reproduces the Jain quasielectron wave function and elucidates the difference between the Jain and Laughlin quasielectrons.
Russian doll spectrum in a non-Abelian string-net ladder
NASA Astrophysics Data System (ADS)
Schulz, Marc Daniel; Dusuel, Sébastien; Vidal, Julien
2015-04-01
We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark contrast with the ones obtained for Fibonacci or Ising theories.
Non-Abelian, supersymmetric black holes and strings in 5 dimensions
NASA Astrophysics Data System (ADS)
Meessen, Patrick; Ortín, Tomás; Ramírez, Pedro F.
2016-03-01
We construct and study the first supersymmetric black-hole and black-string solutions of non-Abelian-gauged {N}=1 , d = 5 supergravity ({N}=1 , d = 5 Super-Einstein-Yang-Mills theory) with non-trivial SU(2) gauge fields: BPST instantons for black holes and BPS monopoles of different kinds ('t Hooft-Polyakov, Wu-Yang and Protogenov) for black strings and also for certain black holes that are well defined solutions only for very specific values of all the moduli. Instantons, as well as colored monopoles do not contribute to the masses and tensions but do contribute to the entropies.
Mimetic discretization of the Abelian Chern-Simons theory and link invariants
Di Bartolo, Cayetano; Grau, Javier; Leal, Lorenzo
2013-12-15
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.
Molecular Eigensolution Symmetry Analysis and Fine Structure
Harter, William G.; Mitchell, Justin C.
2013-01-01
Spectra of high-symmetry molecules contain fine and superfine level cluster structure related to J-tunneling between hills and valleys on rovibronic energy surfaces (RES). Such graphic visualizations help disentangle multi-level dynamics, selection rules, and state mixing effects including widespread violation of nuclear spin symmetry species. A review of RES analysis compares it to that of potential energy surfaces (PES) used in Born–Oppenheimer approximations. Both take advantage of adiabatic coupling in order to visualize Hamiltonian eigensolutions. RES of symmetric and D2 asymmetric top rank-2-tensor Hamiltonians are compared with Oh spherical top rank-4-tensor fine-structure clusters of 6-fold and 8-fold tunneling multiplets. Then extreme 12-fold and 24-fold multiplets are analyzed by RES plots of higher rank tensor Hamiltonians. Such extreme clustering is rare in fundamental bands but prevalent in hot bands, and analysis of its superfine structure requires more efficient labeling and a more powerful group theory. This is introduced using elementary examples involving two groups of order-6 (C6 and D3~C3v), then applied to families of Oh clusters in SF6 spectra and to extreme clusters. PMID:23344041
Quantum phase transition of ultracold bosons in the presence of a non-Abelian synthetic gauge field
Grass, T.; Saha, K.; Sengupta, K.; Lewenstein, M.
2011-11-15
We study the Mott phases and the superfluid-insulator transition of two-component ultracold bosons on a square optical lattice in the presence of a non-Abelian synthetic gauge field, which renders a SU(2)-hopping matrix for the bosons. Using a resummed hopping expansion, we calculate the excitation spectra in the Mott insulating phases and demonstrate that the superfluid-insulator phase boundary displays a nonmonotonic dependence on the gauge-field strength. We also compute the momentum distribution of the bosons in the presence of the non-Abelian field and show that they develop peaks at nonzero momenta as the superfluid-insulator transition point is approached from the Mott side. Finally, we study the superfluid phases near the transition and discuss the induced spatial pattern of the superfluid density due to the presence of the non-Abelian gauge potential.
Detailed study of the Abelian-projected SU(2) flux tube and its dual Ginzburg-Landau analysis
NASA Astrophysics Data System (ADS)
Koma, Y.; Koma, M.; Ilgenfritz, E.-M.; Suzuki, T.
2003-12-01
The color-electric flux tube of Abelian-projected (AP) SU(2) lattice gauge theory in the maximally Abelian gauge (MAG) is examined. It is shown that the lattice Gribov copy effect in the MAG is crucial for the monopole-related parts of the flux-tube profiles. Taking into account both the gauge fixing procedure and the effect of finite quark-antiquark distance properly, the scaling property of the flux-tube profile is confirmed. The quantitative relation between the measured AP flux tube and the flux-tube solution of the U(1) dual Abelian Higgs (DAH) model is also discussed. The fitting of the AP flux tube in terms of the DAH flux tube indicates that the vacuum can be classified as a weakly type-I dual superconductor.
Symmetry Guide to Ferroaxial Transitions.
Hlinka, J; Privratska, J; Ondrejkovic, P; Janovec, V
2016-04-29
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO_{2}, LuFe_{2}O_{4}, and URu_{2}Si_{2}.
Symmetry Guide to Ferroaxial Transitions
NASA Astrophysics Data System (ADS)
Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.
2016-04-01
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
Radiating stars with exponential Lie symmetries
NASA Astrophysics Data System (ADS)
Mohanlal, R.; Maharaj, S. D.; Tiwari, Ajey K.; Narain, R.
2016-07-01
We analyze the general model of a radiating star in general relativity. A group analysis of the under determined, nonlinear partial differential equation governing the model's gravitational potentials is performed. This analysis is an extension of previous group analyses carried out and produces new group invariant solutions. We find that the gravitational potentials depend on exponential functions owing to the choice of the Lie symmetry generator. The fundamental boundary equation to be solved is in general a Riccati equation. Several new exact families of solutions to the boundary condition are generated. Earlier models of Euclidean stars and generalized Euclidean stellar models are regained as special cases. Linear equations of state can be found for shear-free and shearing spacetimes.
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-01
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.
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-01
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. PMID:23215268
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Non-Abelian electric-magnetic duality with supersymmetry in 4D and 10D
NASA Astrophysics Data System (ADS)
Nishino, Hitoshi; Rajpoot, Subhash
2015-10-01
We present electric-magnetic (Hodge) duality formulation for non-Abelian gauge groups with N =1 supersymmetry in 3 +1 (4D) dimensions. Our system consists of three multiplets: (i) A super-Yang-Mills vector multiplet (YMVM) (Aμ I,λI) , (ii) a dual vector multiplet (DVM) (Bμ I,χI) , and (iii) an unphysical tensor multiplet (TM) (Cμν I,ρI,φI) , with the index I for adjoint representation. The multiplets YMVM and DVM are dual to each other like: Gμν I=(1 /2 )ɛμν ρ σFρσ I . The TM is unphysical, but still plays an important role for establishing the total consistency of the system, based on recently developed tensor-hierarchy formulation. We also apply this technique to non-Abelian electric-magnetic duality in 9 +1 (10D) dimensions. The extra bosonic auxiliary field Kμ1⋯μ6 in 10D is shown to play an important role for the closure of supersymmetry on fields.
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.
Experimental realization of non-abelian geometric gates with a superconducting three-level system
NASA Astrophysics Data System (ADS)
Abdumalikov, Abdufarrukh; Fink, J. M.; Juliusson, K.; Pechal, M.; Berger, S.; Wallraff, A.; Filipp, S.
2013-03-01
Geometric gates hold promise to provide the building blocks for robust quantum computation. In our experiments, we use a superconducting three-level system (transmon) to realize non-adiabatic non-abelian geometric gates. As computational basis we choose the ground and second excited states, while the first excited state acts as an ancilla state. The gates are realized by applying two resonant drives between the transmon levels. During the geometric gate ration of the amplitudes of the two drive tone is kept constant. Different gates are obtained for different ratio of the drive tones. We implement a Hadamard, a NOT and a phase gates with the fidelities of 95 % , 98 % , and 97 % as determined by full process tomography and maximum likelihood methods. We explicitly show the non-abelian nature of gates by applying two non-commuting gates in alternating order. The demonstrated holonomic gates are not exclusive to superconducting quantum devices, but can also be applied to other three level systems with similar energy level structure.
Superstring theory on smooth manifolds with a non-abelian lie group as covering space
NASA Astrophysics Data System (ADS)
Fré, P.; Gliozzi, F.
1989-11-01
In this paper we develop superstring theory on target spaces M target = M 4 ⊗ G/B where G is a non-abelian Lie-group and B ⊂ G is a suitable discrete subgroup. These target spaces, different from orbifolds, are smooth differentiable manifolds. Nontrivial choices of B give rise to twisted Kač-Moody algebras providing the mechanism which allows the existence of massless fermions in the string spectrum notwithstanding the non-abelian character of G. Actually we show that there is a unique choice of the group G compatible with the requirement of massless fermion existence, two-dimensional conformal invariance and finally with N = 1 target supersymmetry. It is G = SU(2) 3. We discuss modular invariance and Goddard-Nahm-Olive fermionization. We show that at the quantum level we can describe the SU(2) 3 theory by means of 18 free fermions belonging to the adjoint representation of SU(2) 6. This enables us to make contact with the free fermion approach. However our group interpretation provides additional constraints on the permissible boundary conditions for free fermion theories admitting a geometrical interpretation as σ-models on a smooth manifold: the G/B space. Finally the choice of B is related to the number of space-time supersymmetries.
Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
NASA Astrophysics Data System (ADS)
Zhang, Yuhe; Sreejith, G. J.; Jain, J. K.
2015-08-01
The possibility of realizing bosonic fractional quantum Hall effect in ultracold atomic systems suggests a new route to producing and manipulating anyons, by introducing auxiliary bosons of a different species that capture quasiholes and thus inherit their nontrivial braiding properties. States with localized quasiholes at any desired locations can be obtained by annihilating the auxiliary bosons at those locations. We explore how this method can be used to generate non-Abelian quasiholes of the Moore-Read Pfaffian state for bosons at filling factor ν =1 . We show that a Hamiltonian with an appropriate three-body interaction can produce two-quasihole states in two distinct fusion channels of the topological "qubit." Characteristics of these states that are related to the non-Abelian nature can be probed and verified by a measurement of the effective relative angular momentum of the auxiliary bosons, which is directly related to their pair distribution function. Moore-Read states of more than two quasiholes can also be produced in a similar fashion. We investigate some issues related to the experimental feasibility of this approach, in particular, how large the systems should be for a realization of this physics and to what extent this physics carries over to systems with the more standard two-body contact interaction.
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.
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.
NASA Astrophysics Data System (ADS)
Goldman, N.; Gerbier, F.; Lewenstein, M.
2013-07-01
We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser-coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depicts a chequerboard structure, allowing for laser-assisted tunnelling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a ‘flavour’ quantum number undergoing non-Abelian tunnelling along nearest-neighbour links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighbouring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunnelling techniques. We demonstrate that a simple mapping allows us to express this model in terms of matrix hopping operators that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunnelling methods applied to the chequerboard optical lattice.
A solenoidal synthetic field and the non-Abelian Aharonov-Bohm effects in neutral atoms
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
Non-Abelian states in Fractional Quantum Hall effect in charge carrier hole systems
NASA Astrophysics Data System (ADS)
Simion, George; Lyanda-Geller, Yuli
Quasiparticle excitations obeying non-Abelian statistics represent the key element of topological quantum computing. Crossing of levels and strong coupling between angular momentum and orbital motion, described by Luttinger Hamiltonian, make properties of charge carrier holes different from those of electrons. Peculiarities of hole spectrum in magnetic field provide an opportunity for controlling Landau level mixing in charge carier hole systems. In order to describe Fractional Quantum Hall effect for holes, we propose a method to map hole spectrum and wavefunctions using a spherical shell. We investigate the experimentally observed ν = 1 / 2 state in spherical geometry. Haldane pseudopotentials are computed and the effect of Landau level mixing is evaluated. Exact diagonalization of Coulomb interaction in systems with eight to fourteen holes is performed. We determine that the ground state superposition with Abelian 331 state is very small and the overlap with Moore-Read state is significant. The quasihole and quasielectron excitations are discussed. Research was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0010544.
Non-Abelian vortex in four dimensions as a critical string on a conifold
NASA Astrophysics Data System (ADS)
Koroteev, P.; Shifman, M.; Yung, A.
2016-09-01
Non-Abelian vortex strings supported in a certain four-dimensional N =2 Yang-Mills theory with fundamental matter were shown [1] to become critical superstrings. In addition to translational moduli, the non-Abelian strings under consideration carry orientational and size moduli. Their dynamics is described by the two-dimensional sigma model whose target space is a tautological bundle over the complex projective space. For the N =2 theory with the U (2 ) gauge group and four fundamental hypermultiplets, there are six orientational and size moduli. After combining with four translational moduli, they form a ten-dimensional target space, which is required for a superstring to be critical. For the theory in question, the target space of the sigma model is C2×Y6, where Y6 is a conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of the 4D bulk N =2 theory. It turns out that most of the states arising from the ten-dimensional graviton spectrum are nondynamical in 4D. We find a single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold. We interpret this degree of freedom as a monopole-monopole baryon of the 4D theory (at strong coupling).
Das Sarma, Sankar
2012-10-03
I will discuss the revolutionary new concept of topological quantum computation, which is fault-tolerant at the hardware level with no need, in principle, of any quantum error correction protocols. Errors simply do not occur since the physical qubits and the computation steps are protected against decoherence by non-local topological correlations in the underlying physical system. The key idea is non-Abelian statistics of the quasiparticles (called 'anyons' as opposed to fermions or bosons), where the space-time braiding of the anyons around each other, i.e. quantum 'knots', form topologically protected quantum gate operations. I will describe in detail the theoretical principles guiding the experimental search for the appropriate topological phases of matter where such non-Abelian anyons, which are low-dimensional solid state versions of the elusive and exotic Majorana fermions hypothesized seventy-five years ago, may exist. I will critically discuss the recent experimental claims of observing the Majorana modes in semiconductor nanowire structures following earlier theoretical proposals, outlining the future developments which would be necessary to eventually build a topological quantum computer.
The primordial curvature perturbation from vector fields of general non-Abelian groups
Karciauskas, Mindaugas
2012-01-01
We consider the generation of primordial curvature perturbation by general non-Abelian vector fields without committing to a particular group. Self-interactions of non-Abelian fields make the field perturbation non-Gaussian. We calculate the bispectrum of the field perturbation using the in-in formalism at tree level. The bispectrum is dominated by the classical evolution of fields outside the horizon. In view of this we show that the dominant contribution can be obtained from the homogeneous classical equation of motion. Then we calculate the power spectrum of the curvature perturbation. The anisotropy in spectrum is suppressed by the number of fields. This makes it possible for vector fields to be responsible for the total curvature perturbation in the Universe without violating observational bounds on statistical anisotropy. The bispectrum of the curvature perturbation is also anisotropic. Finally we give an example of the end-of-inflation scenario in which the curvature perturbation is generated by vector gauge fields through varying gauge coupling constant(s), which in covariant derivatives couples the Higgs field to the vector fields. We find that reasonably large gauge groups may result in the observable anisotropy in the power spectrum of the curvature perturbation.
Non-abelian fractional quantum hall effect for fault-resistant topological quantum computation.
Pan, Wei; Thalakulam, Madhu; Shi, Xiaoyan; Crawford, Matthew; Nielsen, Erik; Cederberg, Jeffrey George
2013-10-01
Topological quantum computation (TQC) has emerged as one of the most promising approaches to quantum computation. Under this approach, the topological properties of a non-Abelian quantum system, which are insensitive to local perturbations, are utilized to process and transport quantum information. The encoded information can be protected and rendered immune from nearly all environmental decoherence processes without additional error-correction. It is believed that the low energy excitations of the so-called =5/2 fractional quantum Hall (FQH) state may obey non-Abelian statistics. Our goal is to explore this novel FQH state and to understand and create a scientific foundation of this quantum matter state for the emerging TQC technology. We present in this report the results from a coherent study that focused on obtaining a knowledge base of the physics that underpins TQC. We first present the results of bulk transport properties, including the nature of disorder on the 5/2 state and spin transitions in the second Landau level. We then describe the development and application of edge tunneling techniques to quantify and understand the quasiparticle physics of the 5/2 state.
Anomalous Slow Fidelity Decay for Symmetry-Breaking Perturbations
NASA Astrophysics Data System (ADS)
Gorin, T.; Kohler, H.; Prosen, T.; Seligman, T. H.; Stöckmann, H.-J.; Žnidarič, M.
2006-06-01
Symmetries as well as other special conditions can cause anomalous slowing down of fidelity decay. These situations will be characterized, and a family of random matrix models to emulate them generically presented. An analytic solution based on exponentiated linear response will be given. For one representative case the exact solution is obtained from a supersymmetric calculation. The results agree well with dynamical calculations for a kicked top.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Monster symmetry and extremal CFTs
NASA Astrophysics Data System (ADS)
Gaiotto, Davide
2012-11-01
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.
2008-11-01
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.
Froggatt-Nielsen models with a residual Z4R symmetry
NASA Astrophysics Data System (ADS)
Dreiner, Herbi K.; Opferkuch, Toby; Luhn, Christoph
2013-12-01
The Froggatt-Nielsen mechanism provides an elegant explanation for the hierarchies of fermion masses and mixings in terms of a U(1) symmetry. Promoting such a family symmetry to an R symmetry, we explicitly construct supersymmetric Froggatt-Nielsen models which are gauged, family-dependent U(1)R completions of the Z4R symmetry proposed by Lee, Raby, Ratz, Ross, Schieren, Schmidt-Hoberg and Vaudrevange in 2010. Forbidden by Z4R, the μ term is generated around the supersymmetry breaking scale m3/2 from either the Kähler potential or the superpotential. Neutrinos acquire their mass via the type-I seesaw mechanism with three right-handed neutrino superfields. Taking into account the Green-Schwarz anomaly cancellation conditions, we arrive at a total of 3×34 distinct phenomenologically viable charge assignments for the standard model fields, most of which feature highly fractional charges.
Bufetov, Aleksandr I; Gurevich, Boris M
2011-07-31
The main result of the paper is the statement that the 'smooth' measure of Masur and Veech is the unique measure of maximal entropy for the Teichmueller flow on the moduli space of Abelian differentials. The proof is based on the symbolic representation of the flow in Veech's space of zippered rectangles. Bibliography: 29 titles.
NASA Astrophysics Data System (ADS)
Kazakov, Alexander; Kolkovsky, V.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Rokhinson, Leonid
2015-03-01
Several experiments detected signatures of Majorana fermions in nanowires, and the focus of current research is shifting toward systems where non-Abelian statistics of excitations can be demonstrated. To achieve this goal we are developing a new platform where non-Abelian excitations can be created and manipulated in a two-dimensional plane, with support for Majorana and higher order non-Abelian excitations. The system is based on CdTe quantum wells non-uniformly doped with paramagnetic impurities, which result in a complicate field-dependence of Zeeman splitting. A unique property of the system is that at high fields we can form a quantum Hall ferromagnet with gate-controllable spin polarization. Helical 1D edge channels formed along the edges of electrostatic gates may support generalized non-Abelian excitations in the fractional qunatum Hall regime, and Majorana and parafermion excitations in the presence of induced superconductivity. We will present results on the gate control of s-d exchange in specially designed heterostructures, demonstrate gate control of spin polarization at filling factor ν = 2 , and show spatial separation of quantum Hall states with different spin polarization using lithographically defined gates.
NASA Astrophysics Data System (ADS)
Gavrilov, S. P.; Gitman, D. M.
1993-05-01
We obtain explict expressions of all types of Green's functions in the Furry picture of the electroweak theory with a free, non-Abelian external field, by solving the corresponding one-particle equations. We also give the expressions for the matrix elements of simple processes in an external field.
Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations.
Yurovsky, Vladimir A
2014-11-14
Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to nontrivial permutation symmetries (beyond the conventional paradigm of symmetric-antisymmetric states). The present work obtains the following. (a) Selection rules for additional nonseparable (dependent on spins and coordinates) k-body interactions: the Young diagrams, associated with the initial and final states of a transition, can differ by relocation of no more than k boxes between their rows. (b) Correlation rules in which eigenstate-averaged local correlations of k particles vanish if k exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry-in 1929, Dirac identified those with characters of the symmetric group-relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Snake states and their symmetries in graphene
NASA Astrophysics Data System (ADS)
Tiwari, Rakesh; Liu, Yang; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.
Snake states are open trajectories for charged particles moving in two dimensions under the influence of a spatially varying perpendicular magnetic field. They can also occur in a constant perpendicular magnetic field when the particle density is made nonuniform as realized at a pn junction in a semiconductor, or in graphene. We examine the correspondence of such trajectories in monolayer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric perpendicular magnetic field and (b) antisymmetric carrier density distribution in a uniform perpendicular magnetic field. Although, these families support different internal symmetries, the pattern of the boundary and interface currents is the same in both cases. We demonstrate that these two physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these two problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p-wave paired state.
Snake states and their symmetries in graphene
NASA Astrophysics Data System (ADS)
Liu, Yang; Tiwari, Rakesh P.; Brada, Matej; Bruder, C.; Kusmartsev, F. V.; Mele, E. J.
2015-12-01
Snake states are open trajectories for charged particles propagating in two dimensions under the influence of a spatially varying perpendicular magnetic field. In the quantum limit they are protected edge modes that separate topologically inequivalent ground states and can also occur when the particle density rather than the field is made nonuniform. We examine the correspondence of snake trajectories in single-layer graphene in the quantum limit for two families of domain walls: (a) a uniform doped carrier density in an antisymmetric field profile and (b) antisymmetric carrier distribution in a uniform field. These families support different internal symmetries but the same pattern of boundary and interface currents. We demonstrate that these physically different situations are gauge equivalent when rewritten in a Nambu doubled formulation of the two limiting problems. Using gauge transformations in particle-hole space to connect these problems, we map the protected interfacial modes to the Bogoliubov quasiparticles of an interfacial one-dimensional p -wave paired state. A variational model is introduced to interpret the interfacial solutions of both domain wall problems.
Three-family unification in higher dimensional models
Mimura, Yukihiro; Nandi, S.
2009-05-01
In orbifold models, gauge, Higgs, and the matter fields can be unified in one multiplet from the compactification of higher dimensional supersymmetric gauge theory. We study how three families of chiral fermions can be unified in the gauge multiplet. The bulk gauge interaction includes the Yukawa interactions to generate masses for quarks and leptons after the electroweak symmetry is broken. The bulk Yukawa interaction has global or gauged flavor symmetry originating from the R symmetry or bulk gauge symmetry, and the Yukawa structure is restricted. When the global and gauged flavor symmetries are broken by orbifold compactification, the remaining gauge symmetry which contains the standard model gauge symmetry is restricted. The restrictions from the bulk flavor symmetries can provide explanations of fermion mass hierarchy.
Predicting lepton flavor mixing from Δ(48) and generalized CP symmetries
NASA Astrophysics Data System (ADS)
Ding, Gui-Jun; Zhou, Ye-Ling
2015-02-01
We propose to understand the mixing angles and CP-violating phases from the Δ(48) family symmetry combined with the generalized CP symmetry. A model-independent analysis is performed by scanning all the possible symmetry breaking chains. We find a new mixing pattern with only one free parameter, excellent agreement with the observed mixing angles can be achieved and all the CP-violating phases are predicted to take nontrivial values. This mixing pattern is testable in the near future neutrino oscillation and neutrinoless double-beta decay experiments. Finally, a flavor model is constructed to realize this mixing pattern. Supported by National Natural Science Foundation of China (11275188, 11179007, 11135009)
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
Symmetry Engineering of Graphene Plasmonic Crystals.
Yeung, Kitty Y M; Chee, Jingyee; Song, Yi; Kong, Jing; Ham, Donhee
2015-08-12
The dispersion relation of plasmons in graphene with a periodic lattice of apertures takes a band structure. Light incident on this plasmonic crystal excites only particular plasmonic modes in select bands. The selection rule is not only frequency/wavevector matching but also symmetry matching, where the symmetry of plasmonic modes originates from the point group symmetry of the lattice. We demonstrate versatile manipulation of light-plasmon coupling behaviors by engineering the symmetry of the graphene plasmonic crystal.
Noether symmetries and duality transformations in cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Superalgebra and fermion-boson symmetry
Miyazawa, Hironari
2010-01-01
Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Facial symmetry in robust anthropometrics.
Kalina, Jan
2012-05-01
Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function.
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
Symmetry breaking around a wormhole
NASA Astrophysics Data System (ADS)
Choudhury, A. L.
1996-11-01
We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.
Lepton mixing and discrete symmetries
NASA Astrophysics Data System (ADS)
Hernandez, D.; Smirnov, A. Yu.
2012-09-01
The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4, and A5. We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S4 model and reproduces the allowed values of the mixing angles, we predict δ=(90°-120°).
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Gleiser, Marcelo; Stamatopoulos, Nikitas; Graham, Noah
2010-08-15
Through a detailed numerical investigation in three spatial dimensions, we demonstrate that long-lived time-dependent field configurations emerge dynamically during symmetry breaking in an expanding de Sitter spacetime. We investigate two situations: a single scalar field with a double-well potential and an SU(2) non-Abelian Higgs model. For the single scalar, we show that large-amplitude oscillon configurations emerge spontaneously and persist to contribute about 1.2% of the energy density of the Universe. We also show that for a range of parameters, oscillon lifetimes are enhanced by the expansion and that this effect is a result of parametric resonance. For the SU(2) case, we see about 4% of the final energy density in oscillons.
CP phases of neutrino mixing in a supersymmetric B-L gauge model with T7 lepton flavor symmetry
NASA Astrophysics Data System (ADS)
Ishimori, Hajime; Khalil, Shaaban; Ma, Ernest
2012-07-01
In a recently proposed renormalizable model of neutrino mixing using the non-Abelian discrete symmetry T7 in the context of a supersymmetric extension of the standard model with gauged U(1)B-L, a correlation was obtained between θ13 and θ23 in the case where all four parameters are real. Here we consider one parameter to be complex, thus allowing for one Dirac CP phase δCP and two Majorana CP phases α1,2. We find a slight modification to this correlation as a function of δCP. For a given set of input values of Δm212, Δm322, θ12, and θ13, we obtain sin22θ23 and mee (the effective Majorana neutrino mass in neutrinoless double beta decay) as functions of tanδCP. We find that the structure of this model always yields small |tanδCP|.
Chiral symmetry and nucleon structure
Holstein, B.R. . Dept. of Physics and Astromony Washington Univ., Seattle, WA . Inst. for Nuclear Theory)
1992-01-01
Recently it has been realized that significant tests of the validity of QCD are available in low energy experiments (E < 500 MeV) by exploiting the property of (broken) chiral symmetry. This technique has been highly developed in The Goldstone boson sector by the work of Gasser and Leutwyler. Application to the nucleon system is much more difficult and is now being carefully developed.
Non-Abelian cosmic strings in de Sitter and anti-de Sitter space
NASA Astrophysics Data System (ADS)
Santos, Antônio de Pádua; Bezerra de Mello, Eugênio R.
2016-09-01
In this paper we investigate the non-Abelian cosmic string in de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also of the metric tensor for specific values of the physical parameters of the theory. For the de Sitter case, we find the appearance of an horizon. This horizon is consequence of the presence of the cosmological constant, and its position strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (00) and (z z ) components of the metric tensor. They present a strong increasing behavior for large distance from the string.
Topological phase transitions with non-Abelian gauge potentials on square lattices
NASA Astrophysics Data System (ADS)
Chen, Yao-Hua; Li, Jian; Ting, C. S.
2013-11-01
We investigate the topological phase transition on interacting square lattices via the non-Abelian potential by employing the real-space cellular dynamical mean-field theory combining with the continuous-time Monte Carlo method. For a weak on-site Hubbard interaction, a topological band insulating state with a pair of gapless edge states is induced by a next-nearest-neighbor hopping. A phase transition from the metallic phase to the Mott insulating phase is observed when the interaction is increased. These two phases can be distinguished by detecting whether a bulk gap in the K-dependent spectral function exists. The whole phase diagrams as functions of the interaction, next-nearest-neighbor hopping energy, and temperature are presented. The experimental setup to observe these new interesting phase transitions is also discussed.
Non-perturbative particle production mechanism in time-dependent strong non-Abelian fields
Levai, Peter; Skokov, Vladimir V.
2011-04-26
Non-perturbative production of quark-antiquarks is investigated in the early stage of heavy-ion collisions. The time-dependent study is based on a kinetic description of the fermion-pair production in strong non-Abelian fields. We introduce time-dependent chromo-electric external field with a pulse-like time evolution to simulate the overlap of two colliding heavy ions. We have found that the small inverse duration time of the field pulse determines the efficiency of the quark-pair production. The expected suppression for heavy quark production, as follows from the Schwinger formula for a constant field, is not seen, but an enhanced heavy quark production appears at ultrarelativistic energies. We convert our pulse duration time-dependent results into collisional energy dependence and introduce energy and flavour-dependent string tensions, which can be used in string based model calculations at RHIC and LHC energies.
Beta function in the non-Abelian Nambu-Jona-Lasinio model in four dimensions
Alves, Van Sergio; Pinheiro, S. V. L.; Nascimento, Leonardo; Pena, Francisco
2009-08-15
In this paper we present the structure of the renormalization group in non-Abelian Nambu-Jona-Lasinio model up to 1-loop order. The model is not perturbatively renormalizable in the usual power counting sense, but it is treated as an effective theory, valid in a scale of energy in which p<<{lambda}, where p is the external momenta of the loop and {lambda} is a massive parameter that characterizes the couplings of the nonrenormalizable vertex. We clarify the tensorial structure of the interaction vertices and calculate the functions of the renormalization group. The analysis of the fixed points of the theory is also presented using Zimmermann's procedure for reducing the coupling constants. We find that the origin is an infrared-stable fixed point at low energies and also there is a nontrivial ultraviolet stable fixed point, indicating that the theory could be perturbatively investigated in the low momentum regime.