Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues

TL;DR

This paper investigates the effective potential of SU(2) gauge theory's Polyakov loops and Wilson loop eigenvalues across a range of temperatures, using simulations and a simple parametrization model.

Contribution

It introduces a model to parametrize the effective potential of Polyakov loops and Wilson loop eigenvalues in SU(2) gauge theory based on simulation data.

Findings

Effective potential for Polyakov loops extracted from simulations.

A simple parametrization model including Vandermonde and polynomial terms.

Insights into the behavior of Wilson loop eigenvalues at different temperatures.

Abstract

We simulate SU(2) gauge theory at temperatures ranging from slightly below $T_c$ to roughly $2T_c$ for two different values of the gauge coupling. Using a histogram method, we extract the effective potential for the Polyakov loop and for the phases of the eigenvalues of the thermal Wilson loop, in both the fundamental and adjoint representations. We show that the classical potential of the fundamental loop can be parametrized within a simple model which includes a Vandermonde potential and terms linear and quadratic in the Polyakov loop. We discuss how parametrizations for the other cases can be obtained from this model.