Vortices and confinement in hot and cold D=2+1 gauge theories

TL;DR

This paper investigates how vortex free energy varies with temperature in D=2+1 SU(2) gauge theories, revealing its relation to confinement phenomena both below and above the deconfining transition.

Contribution

It provides numerical evidence linking vortex properties to confinement and spatial string tension across the deconfining transition in lattice gauge theories.

Findings

Vortex free energy is zero at large volumes for all T.

Below Tc, the phase is linearly confining; above Tc, spatial confinement persists.

The decrease of vortex free energy with volume is governed by the spatial string tension.

Abstract

We calculate the variation with temperature of the vortex free energy in D=2+1 SU(2) lattice gauge theories. We do so both above and below the deconfining transition at T=Tc. We find that this quantity is zero at all T for large enough volumes. For T<Tc this observation is consistent with the fact that the phase is linearly confining; while for T>Tc it is consistent with the conventional expectation of `spatial' linear confinement. In small spatial volumes this quantity is shown to be non-zero. The way it decreases to zero with increasing volume is shown to be controlled by the (spatial) string tension and it has the functional form one would expect if the vortices being studied were responsible for the confinement at low T, and for the `spatial' confinement at large T. We also discuss in detail some of the direct numerical evidence for a non-zero spatial string tension at high T, and we show that the observed linearity of the (spatial) potential extends over distances that are large compared to typical high-T length scales.