Wilson loops in finite Abelian lattice gauge theories

TL;DR

This paper analyzes Wilson loops in finite Abelian lattice gauge theories, providing leading-order expectations in the weak coupling regime without relying on duality or cluster expansions.

Contribution

It extends previous results by computing Wilson loop expectations in $ ext{Z}_n$ lattice gauge theories without duality or cluster expansion methods.

Findings

Computed Wilson loop expectations to leading order in weak coupling regime

Extended and refined previous results by Chatterjee

Did not use duality or cluster expansion techniques

Abstract

We consider lattice gauge theories on $\mathbb{Z}^4$ with Wilson action and structure group $\mathbb{Z}_n$. We compute the expectation of Wilson loop observables to leading order in the weak coupling regime, extending and refining a recent result of Chatterjee. Our proofs use neither duality relations nor cluster expansion techniques.