Deconfinement transition in SU(N) theories from perturbation theory

TL;DR

This paper uses a perturbative approach to analyze the deconfinement transition in SU(N) Yang-Mills theories, successfully capturing phase behavior and transition orders consistent with lattice results.

Contribution

It introduces a simple massive extension of the Landau-DeWitt gauge and computes the one-loop effective potential, providing new insights into the deconfinement transition.

Findings

Correctly describes confining phase at low temperature

Identifies second order transition for N=2

Finds weakly first order transition for N=3

Abstract

We consider a simple massive extension of the Landau-DeWitt gauge for SU($N$) Yang-Mills theory. We compute the corresponding one-loop effective potential for a temporal background gluon field at finite temperature. At this order the background field is simply related to the Polyakov loop, the order parameter of the deconfinement transition. Our perturbative calculation correctly describes a quark confining phase at low temperature and a phase transition of second order for $N=2$ and weakly first order for $N=3$. Our estimates for the transition temperatures are in qualitative agreement with values from lattice simulations or from other continuum approaches. Finally, we discuss the effective gluon mass parameter in relation to the Gribov ambiguities of the Landau-DeWitt gauge.