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.

1+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 (5)

• Bethe/Gauge correspondence on curved spaces
• Gauge/Bethe correspondence from quiver BPS algebras
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Heisenberg Spin Chain And Supersymmetric Gauge Theory
• Langlands Dualities through Bethe/Gauge Correspondence for 3d Gauge Theories