Holomorphic Chern-Simons theory and affine Gaudin models

Abstract

We relate two formalisms recently proposed for describing classical integrable field theories. The first is based on the action of four-dimensional holomorphic Chern-Simons theory introduced and studied by Costello, Witten and Yamazaki. The second makes use of classical generalised Gaudin models associated with untwisted affine Kac-Moody algebras.