A unifying 2D action for integrable $$\sigma$$-models from 4D Chern–Simons theory

Source abstract

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 $$\sigma$$ σ -models which are known to admit descriptions as affine Gaudin models. This includes both the Yang–Baxter deformation and the $$\lambda$$ 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 $$\textsf {E}$$ E -model.