Pure perimeter laws for Wilson lines observables

TL;DR

This paper derives precise asymptotic formulas for Wilson line and loop observables in lattice gauge theories, revealing pure parameter laws in different phases without requiring extreme parameter scaling.

Contribution

It advances previous results by providing detailed asymptotics that do not depend on large or small parameter limits, establishing pure parameter laws in Higgs and confinement phases.

Findings

Wilson line and loop expectations follow pure parameter laws

Asymptotics are valid without extreme parameter scaling

Results apply to Higgs and confinement phases

Abstract

Several recent papers have studied the decay rate of the expectation of Wilson loop and Wilson line observables in lattice gauge theory and the lattice Higgs model. These results have all been perturbative in the sense that the parameters need to scale with the length of the loop or line for the error term to be smaller than the estimate. In this paper, we further develop ideas from~\cite{fv2023} and~\cite{f2024} to give more detailed asymptotics for the expectation of Wilson loop and Wilson line observables, which do not require the parameters to be very large or very small for the error term to be small, thus improving the results of~\cite{flv2022, flv2023, flv2020, f2022b}. In particular, we show that Wilson line and loop observables have a pure parameter law in the Higgs and confinement phases of the lattice Higgs model.