Chern-Simons Theories and Integrability

Abstract: This thesis explores the correspondence between Chern-Simons theory and integrable field theories across different dimensions. It brings together all of my work in this area, including several distinct realizations of this correspondence. The thesis generalizes existing results on four-dimensional Chern-Simons theory and holomorphic Chern-Simons theory on twistor space. Additionally, it presents the discovery of a novel correspondence between five-dimensional holomorphic 2-Chern-Simons theory and integrable field theories in three dimensions.