scholarly journals DYNAMICAL GAUGE SYMMETRY BREAKING AND SUPERCONDUCTIVITY IN THREE-DIMENSIONAL SYSTEMS

1998 ◽  
Vol 13 (13) ◽  
pp. 1019-1033 ◽  
Author(s):  
K. FARAKOS ◽  
N. E. MAVROMATOS
Keyword(s):  
Phase Diagram ◽  
Gauge Theory ◽  
Condensed Matter ◽  
Three Dimensional ◽  
Local Order ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Dependent Parameter ◽  
Dynamical Breaking ◽  
Physical Consequences

We discuss dynamical breaking of non-Abelian gauge groups in three-dimensional (lattice) gauge systems via the formation of fermion condensates. A physically relevant example, motivated by condensed matter physics, is that of a fermionic gauge theory with group SU (2)⊗ U S(1)⊗ U E(1). In the strong U S(1) region, the SU(2) symmetry breaks down to a U(1), due to the formation of a parity-invariant fermion condensate. We conjecture a phase diagram for the theory involving a critical line, which separates the regions of broken SU(2) symmetry from those where the symmetry is restored. In the broken phase, the effective Abelian gauge theory is closely related to an earlier model of two-dimensional parity-invariant superconductivity in doped antiferromagnets. The superconductivity in the model occurs in the Kosterlitz–Thouless mode, since strong phase fluctuations prevent the existence of a local order parameter. Some physical consequences of the SU (2)× U S(1) phase diagram for the (doping-dependent) parameter space of this condensed matter model are briefly discussed.

scholarly journals Exceptional Chern-Simons-Matter dualities

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Kantaro Ohmori
Keyword(s):  
Gauge Theory ◽  
Topological Field Theories ◽  
Time Reversal ◽  
Three Dimensional ◽  
Field Theories ◽  
Chiral Algebra ◽  
Gauge Groups ◽  
Topological Field ◽  
Conformal Embeddings ◽  
Chern Simons

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1}(EN)1↔SU(9−N)−1. Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6},SO(3)8↔PSU(3)−6, are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2}G2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

ASYMPTOTIC COMPLETENESS AND THE THREE-DIMENSIONAL GAUGE THEORY HAVING THE CHERN-SIMON TERM

1989 ◽  
Vol 04 (05) ◽  
pp. 1055-1064 ◽  
Author(s):  
N. NAKANISHI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Three Dimensional ◽  
Asymptotic Completeness ◽  
Higgs Mechanism ◽  
Mass Generation ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Covariant Gauge ◽  
Asymptotic Fields

The three-dimensional Abelian gauge theory having the Chern-Simon term is studied. When matter current is absent, the gauge field in covariant gauge is explicitly expressed in terms of asymptotic fields. It is shown that the mechanism of mass generation can be understood as a kind of the Higgs mechanism.

scholarly journals THE BERRY PHASE AND MONOPOLES IN NON-ABELIAN GAUGE THEORIES

2002 ◽  
Vol 17 (02) ◽  
pp. 157-174 ◽  
Author(s):  
F. V. GUBAREV ◽  
V. I. ZAKHAROV
Keyword(s):  
Gauge Theory ◽  
Wilson Loop ◽  
Continuum Limit ◽  
Gauge Theories ◽  
Berry Phase ◽  
Quantum Mechanical ◽  
Abelian Gauge ◽  
Dynamical Phase ◽  
Physical Consequences ◽  
The Continuum

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorentz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

scholarly journals Localization of Dirac Fermions in Finite-Temperature Gauge Theory

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 194
Author(s):  
Matteo Giordano ◽  
Tamás Kovács
Keyword(s):  
Gauge Theory ◽  
Finite Temperature ◽  
Lattice Gauge Theory ◽  
Dirac Fermions ◽  
Abelian Gauge ◽  
Localization Transition ◽  
Gauge Groups ◽  
Topological Excitations ◽  
Dirac Spectrum ◽  
Lattice Gauge

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

scholarly journals Phases of $$\hbox {QCD}_3$$ with three families of fundamental flavors

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Abdullah Khalil ◽  
Radu Tatar
Keyword(s):  
Phase Diagram ◽  
Gauge Theory ◽  
Three Dimensional ◽  
Fundamental Representation ◽  
The One ◽  
Linear Quantum

AbstractWe explore the phase diagram for an SU(N) gauge theory in $$2 + 1$$ 2 + 1 dimensions with three families of fermions with different masses, all in the fundamental representation. The phase diagram is three dimensional and contains cuboid, planar and linear quantum regions, depending on the values of the fermionic masses. Among other checks, we consider the consistency with boson/fermion dualities and verify the reduction of the phase diagram to the one and two-family diagrams.

scholarly journals Spontaneous parity breaking in three-dimensional non-Abelian gauge theory

1996 ◽  
Vol 54 (2) ◽  
pp. 1826-1830 ◽  
Author(s):  
Hsien-Chung Kao ◽  
Yeong-Chuan Kao ◽  
Yu-Li Lee
Keyword(s):  
Gauge Theory ◽  
Three Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Parity Breaking

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals On the quantization of Seiberg-Witten geometry

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nathan Haouzi ◽  
Jihwan Oh
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Partition Function ◽  
Flat Space ◽  
Matter Content ◽  
Gauge Groups ◽  
Space Limit ◽  
Two Parameters ◽  
Double Quantization ◽  
Quantization Parameters

Abstract We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

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