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

In this article, we provide a short review on the Bethe/gauge correspondence. We first explain the basic idea in an explicit example of the correspondence between XXX spin chains and 2d mathcalN=(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.