Integrability from Homotopy Algebras

Homotopy algebraic methods have become increasingly influential in studying field theories. We begin by introducing the (relative) homotopy Lie algebra perceptive on quantum field theory (assuming no background). We then consider the application of this picture to integrable systems. In particular, we consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model, establishing an explicit quasi-isomorphism between the cyclic L∞-algebras governing both theories which directly gives the Lax connection.