Yang-Mills model in 2D: Old and new

The study of random holonomies (or Wilson loops) of the 2D Yang-Mills model goes back to the late 1980s. The law of these loop observables can be described in terms of heat kernels on Lie groups. In this talk, we start with an introductory review of these ideas. Then we discuss our new result in which we construct a space of singular connections {A}, with a gauge group G acting on it. We show that there is a unique invariant measure for a Langevin dynamic on {A}/G, called the Yang-Mills measure, which has the loop observables described in the earlier works.

This is based on a joint paper with Chandra, Chevyrev, Hairer, and a more recent paper with Chevyrev.