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

TL;DR

This review discusses the Bethe/Gauge correspondence, illustrating its connection to integrability in supersymmetric gauge theories through examples like spin chains and partition functions, highlighting recent insights into their algebraic structures.

Contribution

It provides an accessible overview of the Bethe/Gauge correspondence, emphasizing explicit examples and exploring the link between 4d and 2d gauge theories and integrable systems.

Findings

Connection between XXX spin chains and 2d gauge theories explained

Comparison of instanton and vortex partition functions explored

Similarity in integrability structures of 4d and 2d gauge theories identified

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.