Wilson loops in the abelian lattice Higgs model

TL;DR

This paper analyzes the expected value of Wilson loops in the lattice Higgs model with abelian gauge group, providing leading order calculations and relating them to simpler models like the Ising model.

Contribution

It introduces a method to compute Wilson loop expectations in the lattice Higgs model by relating it to the $\mathbb{Z}_n$ model and constructs a coupling between these models.

Findings

Leading order expectation of Wilson loops expressed via $\mathbb{Z}_n$ model quantities.

Reduction to the Ising model when $n=2$.

Construction of a coupling between the Higgs and $\mathbb{Z}_n$ models.

Abstract

We consider the lattice Higgs model on $\mathbb{Z}^4$, with structure group given by $ \mathbb{Z}_n $ for $ n \geq 2 $. We compute the expected value of the Wilson loop observable to leading order when the gauge coupling constant and hopping parameter are both sufficiently large. The leading order term is expressed in terms of a quantity arising from the related but much simpler $ \mathbb{Z}_n $ model, which reduces to the Ising model when $n=2$. As part of the proof, we construct a coupling between the lattice Higgs model and the $ \mathbb{Z}_n $ model.