A unifying 2D action for integrable σ -models from 4D Chern–Simons theory

Abstract

In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable σ-models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the λ-deformation of the principal chiral model. We also give an interpretation of Poisson–Lie T-duality in this setting and derive the action of the E-model.