A new derivation of the finite N master loop equation for lattice Yang-Mills

Abstract

. We give a new derivation of the finite N master loop equation for lattice Yang-Mills theory with structure group SO ( N ), U ( N ) or SU ( N ). The SO ( N ) case was initially proved by Chatterjee in [Cha19a], and SU ( N ) was analyzed in a follow-up work by Jafarov [Jaf16]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itˆo’s formula.