Wilson lines in the lattice Higgs model at strong coupling

TL;DR

This paper analyzes Wilson line observables in a 4D lattice Higgs model with z_n gauge group at strong coupling, providing asymptotic behavior and perimeter law decay proofs using high-temperature expansion and Poisson approximation.

Contribution

It offers a rigorous asymptotic analysis of Wilson lines in the lattice Higgs model at strong coupling, including a proof of perimeter law decay for positive Higgs coupling.

Findings

Wilson line expectations decay with perimeter law at strong coupling.

Asymptotic behavior of Wilson lines is explicitly computed with error estimates.

Perimeter law holds whenever the Higgs field coupling is positive.

Abstract

We consider the 4D fixed length lattice Higgs model with Wilson action for the gauge field and structure group $\mathbb{Z}_n$. We study Wilson line observables in the strong coupling regime and compute their asymptotic behavior with error estimates. Our analysis is based on a high-temperature representation of the lattice Higgs measure combined with Poisson approximation. We also give a short proof of the folklore result that Wilson line (and loop) expectations exhibit perimeter law decay whenever the Higgs field coupling constant is positive.