2d integrable field theories from 4d Chern-Simons theory

Abstract

In recent years various unifying frameworks for constructing and understanding 2d integrable field theories have emerged. I will review the framework of Costello and Yamazaki which is based on 4d Chern-Simons gauge theory. In particular, I will explain how it can be used to construct a very broad class of 2d integrable field theories known as integrable E-models. If time permits, I will explain the connection to an alternative framework based on Gaudin models associated with affine Kac-Moody algebras. The talk is based on joint works arXiv:1908.07511, arXiv:1909.13824, arXiv:2008.01829, arXiv:2011.13809 and arXiv:2301.09583.