Semi-holographic 4d Chern-Simons Theory

4-dimensional Chern-Simons theory and integrable field theories

These lecture notes concern the semi-holomorphic 4d chern-simons theory and its applications to classical integrable field theories in 2d and in particular integrable sigma-models.We explain how varying the boundary conditions imposed on this 4d theory allows to recover various occurences of integrable sigma-models through thisconstruction, in particular illustrating this on two simple examples: the principal chiral model and its yang-baxter deformation.