Relating Gauge Theories via Gauge/Bethe Correspondence

Abstract

In this note, we use techniques from integrable systems to study relations between gauge theories. The Gauge/Bethe correspondence, introduced by Nekrasov and Shatashvili, identifies the supersymmetric ground states of an N=(2,2) supersymmetric gauge theory in two dimensions with the Bethe states of a quantum integrable system. We make use of this correspondence to relate three different quiver gauge theories which correspond to three different formulations of the Bethe equations of an integrable spin chain called the tJ model.

arXiv comment30 pages, published in JHEP. LaTeX problem corrected

References in corpus (19)

• Phases of $N=2$ Theories In Two Dimensions
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Transcendentality and Crossing
• Supersymmetric Yang-Mills Systems And Integrable Systems
• High energy QCD as a completely integrable model
• Supersymmetric vacua and Bethe ansatz
• Integrable systems and supersymmetric gauge theory
• Quantum integrability and supersymmetric vacua
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Branes and N=2 Theories in Two Dimensions
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c
• Multiscale N=2 SUSY field theories, integrable systems and their stringy/brane origin -- I
• SUSY field theories, integrable systems and their stringy/brane origin -- II
• Relating Field Theories via Stochastic Quantization
• Quantum Crystals and Spin Chains
• Two Dimensional Mirror Symmetry From M-theory
• Classical Spin Chains and Exact Three-dimensional Superpotentials

Cited by in corpus (29)

• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• String theory of the Omega deformation
• M2-brane surface operators and gauge theory dualities in Toda
• The Omega Deformation From String and M-Theory
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• A New 2d/4d Duality via Integrability
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• A slow review of the AGT correspondence
• General Omega Deformations from Closed String Backgrounds
• A 5d/3d duality from relativistic integrable system
• Higgsed network calculus
• Superspin chains and supersymmetric gauge theories
• Superspin chains from superstring theory
• A-twisted correlators and Hori dualities
• The Gauge-Bethe Correspondence and Geometric Representation Theory
• Quantum Integrable Systems from Supergroup Gauge Theories
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Deformed BPS Monopole in Omega-background
• BPS States in the Duality Web of the Omega deformation
• Twisted Masses and Enhanced Symmetries: the A&D Series
• Supersymmetric quiver gauge theories on the lattice
• Topological Vertex/anti-Vertex and Supergroup Gauge Theory
• BPS Monopole Equation in Omega-background
• Surface operators, dual quivers and contours
• Bethe-State Counting and the Witten Index
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• 2D Seiberg-like dualities with an adjoint matter
• Solution of quantum integrable systems from quiver gauge theories
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence