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

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 σ -models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the λ 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 E -model.