Form factors of self-dual gauge theory are equal to correlators of an (extended) celestial chiral algebra. This suggests that these form factors can be computed using the "bootstrap" method familiar from 2d CFTs. The method can also be applied to certain QCD amplitudes, which are built from form-factors of self-dual gauge theory.
In this paper this bootstrap method is applied to compute two-loop all-plus QCD amplitudes, for SU(N) gauge theory with certain special matter content. A closed formula is presented for all single-trace amplitudes.

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: https://arxiv.org/abs/2109.08101. ---- Part of the London Integrability Journal Club. Please register at integrability-london.weebly.com if you are a new participant. The link will be emailed on Tuesday.