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 \cite{Cha}, and $SU(N)$ was analyzed in a follow-up work by Jafarov \cite{Jafar}. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itô's formula.

16 pages

Cited by in corpus (2)

• Stochastic quantisation of Yang-Mills
• A stochastic PDE approach to large N problems in quantum field theory: a survey