Makeenko-Migdal equations for lattice Yang-Mills-Higgs

TL;DR

This paper derives master loop equations for lattice Yang-Mills-Higgs theories with various structure groups, introducing new operations and observables like open Wilson lines, using stochastic calculus methods.

Contribution

It extends the master loop equations to include Higgs fields and open Wilson lines, providing a new recursive framework for lattice gauge theories with matter fields.

Findings

Derived closed-form master loop equations for lattice Yang-Mills-Higgs

Introduced open Wilson lines as new observables

Provided a concise proof using stochastic calculus techniques

Abstract

We derive a form of master loop equations for the lattice Yang-Mills-Higgs theory with structure group $SO(N)$, $U(N)$ or $SU(N)$. Compared to the pure Yang-Mills setting, several new operations arise. In fact, to obtain a closed recursion we must broaden the class of observables to include open Wilson lines. Our approach is based on the conditional Langevin dynamic and yields a concise proof via It\^o's formula.