Bethe/Gauge correspodence: a short review on an aspect of the integrability nature of supersymmetric gauge theories

Abstract

In this article, we provide a short review (written in Chinese) on the Bethe/Gauge correspondence. We first explain the basic idea in an explicit example of the correspondence between XXX spin chains and 2d $\mathcal{N}=(2,2)$ gauge theories. The connection between 4d and 2d will then be explored by comparing the instanton and vortex partition functions. We conclude this article by briefly mentioning the similarity in the integrability structure of 4d gauge theories and 2d ones from an algebraic aspect, and a potential relation between two different integrable systems.

arXiv comment1+12+3 pages, in Chinese; with a plan to extend to a full version in the future; typos modified and footnotes added in v2

References in corpus (25)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supersymmetric Yang-Mills Systems And Integrable Systems
• How Algebraic Bethe Ansatz works for integrable model
• Supersymmetric vacua and Bethe ansatz
• Integrable systems and supersymmetric gauge theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Quantum integrability and supersymmetric vacua
• Quantum Groups and Quantum Cohomology
• Collective fields, Calogero-Sutherland model and generalized matrix models
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Scattering and Thermodynamics of Integrable N=2 Theories
• Bethe/Gauge correspondence on curved spaces
• Fast analytic solver of rational Bethe equations
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Coulomb branches of quiver gauge theories with symmetrizers
• Seiberg-Witten Prepotential From Instanton Counting
• Unification of integrability in supersymmetric gauge theories
• Gauge/Bethe correspondence from quiver BPS algebras
• G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Generalization and Deformation of Drinfeld quantum affine algebras
• Heisenberg Spin Chain And Supersymmetric Gauge Theory
• Langlands Dualities through Bethe/Gauge Correspondence for 3d Gauge Theories