Effective potential for Polyakov loops from a center symmetric effective theory in three dimensions

TL;DR

This paper uses lattice simulations of a three-dimensional, center symmetric effective theory for SU(2) Yang Mills to analyze the effective potential for Polyakov loops, revealing non-analytic features and phase-dependent behavior.

Contribution

It introduces a lattice simulation approach for a center symmetric effective theory with a fuzzy bag term, providing new insights into the Polyakov loop potential in three dimensions.

Findings

Non-analytic contribution in the Polyakov loop potential from simulations.

Mean-field description with quadratic, quartic, and Vandermonde terms.

Phase diagram dependence of the Vandermonde potential.

Abstract

We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for the Wilson line which includes a "fuzzy" bag term to generate non-perturbative fluctuations. The effective potential for the Polyakov loop is extracted from the simulations including all modes of the loop as well as for cooled configuration where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram.