Wilson loops in finite Abelian lattice gauge theories

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.

38 pages, 8 figures