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

Understand

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 $\sigma$-models which are known to admit descriptions as affine Gaudin models.
• This includes both the Yang-Baxter deformation and the $\lambda$-deformation of the principal chiral model.