Adjoint Wilson Line in SU(2) Lattice Gauge Theory

TL;DR

This paper investigates the behavior of the adjoint Wilson line in finite-temperature SU(2) lattice gauge theory, revealing its complex nonperturbative nature at the deconfining phase transition and providing a model-based estimate of its properties.

Contribution

It analyzes the adjoint Wilson line's expectation value at the critical point, highlighting its nonanalytic behavior and formulating the free energy including perturbative and nonperturbative parts.

Findings

The adjoint Wilson line is nonanalytic at the critical point.

The free energy includes a linearly divergent perturbative term and a finite nonperturbative component.

A flux tube model estimates the nonperturbative contribution, aiding in understanding the line's behavior.

Abstract

The behavior of the adjoint Wilson line in finite-temperature, $SU(2)$, lattice gauge theory is discussed. The expectation value of the line and the associated excess free energy reveal the response of the finite-temperature gauge field to the presence of an adjoint source. The value of the adjoint line at the critical point of the deconfining phase transition is highlighted. This is not calculable in weak or strong coupling. It receives contributions from all scales and is nonanalytic at the critical point. We determine the general form of the free energy. It includes a linearly divergent term that is perturbative in the bare coupling and a finite, nonperturbative piece. We use a simple flux tube model to estimate the value of the nonperturbative piece. This provides the normalization needed to estimate the behavior of the line as one moves along the critical curve into the weak coupling region.