QM Research Seminar: 4d Chern-Simons Theory and the Hitchin System

In recent years, 4d Chern-Simons theory has emerged as a unifying framework for a large class of discrete and continuous integrable systems in two dimensions. At the same time, the Hitchin system remains the most important example of integrable systems in two dimensions. This raises a natural question: can 4d Chern-Simons theory provide a new perspective on Hitchin systems?
In this talk, after reviewing some background, I will explain how 4d Chern-Simons theory can be used to derive an action whose field equations coincide with Hitchin’s equations on a closed surface. I will also describe how the symplectic structure on the space of solutions to Hitchin’s equations, in an arbitrary complex structure, can be recovered from the 4d theory. If time permits, I will discuss how the construction can be modified in the presence of ramification associated with non-compact surfaces.