Gauged sigma models from four-dimensional Chern-Simons

Abstract: Several years ago, a new gauge theory called four-dimensional Chern-Simons was introduced by Costello in an attempt to explain the integrability of various two-dimensional models using techniques in gauge theory. My work focuses on the use of four-dimensional Chern-Simons to explain the integrability of two-dimensional sigma models. I will begin by reviewing the construction of the Wess-Zumino-Witten (WZW) model as the boundary theory of three-dimensional Chern-Simons theory as was introduced by Moore and Seiberg. This will allow me to introduce the analogous construction of Costello and Yamazaki, in which two-dimensional sigma models appear as theories on defects in four-dimensional Chern-Simons. This naturally leads to a discussion of my work in which I construct a large class of gauged sigma models by coupling together two four-dimensional Chern-Simons theories. I will argue that the structure of four-dimensional Chern-Simons suggests that these models are integrable and finish by constructing the gauged WZW model and conformal Toda theories. This talk is based on: arxiv.org/abs/2109.08101.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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