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

TL;DR

This paper analyzes Wilson loop expectations in non-abelian gauge theories with a Higgs boson, providing explicit probabilistic representations and computational methods across different disorder regimes.

Contribution

It introduces a novel approach to compute Wilson loop expectations using Poisson random variables and polymer expansion techniques for various disorder levels.

Findings

Explicit Poisson-based representation of Wilson loop expectations.

Efficient computational methods for low and high disorder regimes.

Identification of main contributions from minimal vortices.

Abstract

We consider computations of Wilson loop expectations to leading order at large $\beta$ in the case where a non-abelian 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.