Wilson loop expectations in lattice gauge theories with finite gauge groups

Abstract

Wilson loop expectations at weak coupling are computed to first order, for four dimensional lattice gauge theories with finite gauge groups which satisfy some mild additional conditions. This continues recent work of Chatterjee, which considered the case of gauge group $\mathbb{Z}_2$. The main steps are (1) reducing the first order computation to a problem of Poisson approximation, and (2) using Stein's method to carry out the Poisson approximation.