Wilson Loop Expectations for Non-abelian Finite Gauge Fields Coupled to a Higgs Boson at Low and High Disorder

We consider computations of Wilson loop expectations to leading order at large beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} in the case where a non-abelian finite gauge field interacts with a Higgs boson. By identifying the main order contributions from minimal vortices, we can express the Wilson loop expectations via an explicit Poisson random variable. This paper treats multiple cases of interests, including the Higgs boson at low and high disorder, and finds efficient polymer expansion like computations for each of these regimes.