scholarly journals 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Kee-Seng Png ◽  
Meng-Chwan Tan
Keyword(s):  
Moduli Space ◽  
Sigma Model ◽  
Three Dimensional ◽  
Simons Theory ◽  
Yang Mills ◽  
Pole Type ◽  
Type Boundary ◽  
Chern Simons ◽  
Manifold With Corners ◽  
Chern Simons Theory

Abstract We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d W-algebra symmetry. By embedding four-dimensional Chern-Simons theory in a partial twist of the five-dimensional maximally supersymmetric Yang-Mills theory on a manifold with corners, we argue that this three-dimensional Toda theory is dual to a two-dimensional topological sigma model with A-branes on the moduli space of solutions to the Bogomolny equations. This furnishes a novel 3d-2d correspondence, which, among other mathematical implications, also reveals that modules of the 3d W-algebra are modules for the quantized algebra of certain holomorphic functions on the Bogomolny moduli space.

scholarly journals Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Masazumi Honda ◽  
Naotaka Kubo
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Supersymmetric Theories ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been conjectured that duality cascade occurs in the $$ \mathcal{N} $$ N = 3 supersymmetric Yang-Mills Chern-Simons theory with the gauge group U(N)k × U(N + M)−k coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $$ \mathcal{N} $$ N = 3 supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on S3 partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.

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 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.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

scholarly journals CONSISTENT INTERACTIONS IN A THREE-DIMENSIONAL THEORY WITH TENSOR GAUGE FIELDS OF DEGREES TWO AND THREE

2003 ◽  
Vol 18 (24) ◽  
pp. 4451-4468 ◽  
Author(s):  
SOLANGE-ODILE SALIU
Keyword(s):  
Three Dimensional ◽  
Simons Theory ◽  
Gauge Fields ◽  
Dimensional Theory ◽  
Gauge Symmetries ◽  
Lagrangian Action ◽  
Brst Cohomology ◽  
The Relationship ◽  
Chern Simons ◽  
Chern Simons Theory

All consistent interactions in a three-dimensional theory with tensor gauge fields of degrees two and three are obtained by means of the deformation of the solution to the master equation combined with cohomological techniques. The local BRST cohomology of this model allows the deformation of the Lagrangian action, accompanying gauge symmetries and gauge algebra. The relationship with the Chern–Simons theory is discussed.

A THREE-DIMENSIONAL COVARIANT APPROACH TO MONODROMY (SKEIN RELATIONS) IN CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (32) ◽  
pp. 2747-2751 ◽  
Author(s):  
B. BRODA
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Wilson Loop ◽  
Three Dimensional ◽  
Simons Theory ◽  
Monodromy Operator ◽  
Covariant Approach ◽  
Path Integral Representation ◽  
Chern Simons ◽  
Chern Simons Theory

A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.

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