scholarly journals Vortex solutions of four-fermion theory coupled to a Yang-Mills-Chern-Simons gauge field

1998 ◽  
Vol 58 (8) ◽  
Author(s):  
Hyuk-jae Lee ◽  
Joo Youl Lee ◽  
Jae Hyung Yee
Keyword(s):  
Gauge Field ◽  
Yang Mills ◽  
Vortex Solutions ◽  
Chern Simons

VORTICES IN CURVED SPACE-TIME

1993 ◽  
Vol 08 (38) ◽  
pp. 3665-3672 ◽  
Author(s):  
J.D. EDELSTEIN ◽  
G. LOZANO ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Scalar Curvature ◽  
Gauge Field ◽  
Space Time ◽  
Higgs Model ◽  
Curved Space ◽  
Abelian Higgs Model ◽  
Vortex Solutions ◽  
Chern Simons ◽  
Higgs Scalar

We study an Abelian Higgs model coupled to a background metric. We find Bogomol’nyi equations when the coupling is achieved through an Rɸ2 term (R being the scalar curvature and ɸ the Higgs scalar). Remarkably, these equations coincide with those arising in models where the gauge field dynamics is governed by a Chern-Simons term so that vortex solutions in our system can be related to self-dual Chern-Simons vortices.

scholarly journals GAUGE THEORY DEFORMATIONS AND NOVEL YANG–MILLS CHERN–SIMONS FIELD THEORIES WITH TORSION

2004 ◽  
Vol 01 (04) ◽  
pp. 493-544 ◽  
Author(s):  
STEPHEN C. ANCO
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Covariant Derivative ◽  
Gauge Theories ◽  
Field Theories ◽  
Deformation Method ◽  
Yang Mills ◽  
The Past ◽  
Nonlinear Gauge ◽  
Chern Simons

A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The physical interest in studying deformations is to address uniqueness of known nonlinear interactions of gauge fields and to look systematically for theoretical possibilities for new interactions. Mathematically, the study of deformations aims to understand the rigidity of the nonlinear structure of gauge field theories and to uncover new types of nonlinear geometrical structures. The first part of this paper summarizes and significantly elaborates a field-theoretic deformation method developed in earlier work. Some key contributions presented here are, firstly, that the determining equations for deformation terms are shown to have an elegant formulation using Lie derivatives in the jet space associated with the gauge field variables. Secondly, the obstructions (integrability conditions) that must be satisfied by lowest-order deformations terms for existence of a deformation to higher orders are explicitly identified. Most importantly, a universal geometrical structure common to a large class of nonlinear gauge theory examples is uncovered. This structure is derived geometrically from the deformed gauge symmetry and is characterized by a covariant derivative operator plus a nonlinear field strength, related through the curvature of the covariant derivative. The scope of these results encompasses Yang–Mills theory, Freedman–Townsend theory, and Einstein gravity theory, in addition to their many interesting types of novel generalizations that have been found in the past several years. The second part of the paper presents a new geometrical type of Yang–Mills generalization in three dimensions motivated from considering torsion in the context of nonlinear sigma models with Lie group targets (chiral theories). The generalization is derived by a deformation analysis of linear abelian Yang–Mills Chern–Simons gauge theory. Torsion is introduced geometrically through a duality with chiral models obtained from the chiral field form of self-dual (2+2) dimensional Yang–Mills theory under reduction to (2+1) dimensions. Field-theoretic and geometric features of the resulting nonlinear gauge theories with torsion are discussed.

Electrically and magnetically charged vortices in the Chern–Simons–Higgs theory

2009 ◽  
Vol 465 (2111) ◽  
pp. 3489-3516 ◽  
Author(s):  
Robin Ming Chen ◽  
Yujin Guo ◽  
Daniel Spirn ◽  
Yisong Yang
Keyword(s):  
Boundary Conditions ◽  
Gauge Field ◽  
Open Problem ◽  
Lagrangian Density ◽  
Finite Energy ◽  
Natural Boundary ◽  
Minimization Procedure ◽  
Vortex Solutions ◽  
Natural Boundary Conditions ◽  
Chern Simons

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern–Simons term.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
Author(s):  
Yeong-Chuan Kao ◽  
Hsiang-Nan Li
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Landau Gauge ◽  
Quantum Corrections ◽  
Simons Theory ◽  
Loop Correction ◽  
Loop Contribution ◽  
Yang Mills ◽  
Chern Simons ◽  
Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

scholarly journals CHARGED TOPOLOGICAL SOLITONS IN (4+1)-DIMENSIONAL YMCS THEORY

1992 ◽  
Vol 07 (27) ◽  
pp. 2469-2475
Author(s):  
C. S. AULAKH
Keyword(s):  
Electric Charge ◽  
Five Dimensions ◽  
Topological Solitons ◽  
Yang Mills ◽  
Chern Simons

We show that when a Chern-Simons term is added to the action of SU (N) (N≥3) Yang-Mills theory in five dimensions the usual self-dual topological solitons present in the theory necessarily pick up a (topological) electric charge.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

scholarly journals BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

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