The master loop equation for lattice YM via the Langevin dynamic

The discrete Yang Mills measure was introduced by Wilson (1974), who made several interesting conjectures about the observables of the theory, now known as Wilson loops. Shortly after, `t Hooft (1974) discovered the 1/N expansion of the theory with structure group U(N), inspiring a large body of physics literature known as 'large N problems'. More recently, Chatterjee (2015) studied the large N limit rigorously in the strong coupling regime, and a key tool is the finite N master loop equation, a recursive formula satisfied by Wilson loops.

In this talk, I will discuss the Langevin dynamic associated to the discrete Yang Mills measure and show that Chatterjee's loop equation can be derived as a simple consequence of Ito's formula. This is joint work with Hao Shen and Rongchan Zhu.