Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond

TL;DR

This paper investigates the deconfinement transition in Yang-Mills theories, especially SU(3), using a two-loop background field approach, improving transition temperature estimates and thermodynamic predictions, and exploring other gauge groups.

Contribution

It extends previous SU(2) calculations to SU(3), SU(4), and Sp(2), providing more accurate transition temperatures and thermodynamic behavior, and discusses the role of background fields as order parameters.

Findings

Two-loop corrections improve transition temperature estimates.

Thermodynamic observables like entropy and pressure become positive at all temperatures.

First-order phase transitions are confirmed for SU(3), SU(4), and Sp(2).

Abstract

We study the confinement-deconfinement phase transition of pure Yang-Mills theories at finite temperature using a simple massive extension of standard background field methods. We generalize our recent next-to-leading-order perturbative calculation of the Polyakov loop and of the related background field effective potential for the SU(2) theory to any compact and connex Lie group with a simple Lie algebra. We discuss in detail the SU(3) theory, where the two-loop corrections yield improved values for the first-order transition temperature as compared to the one-loop result. We also show that certain one-loop artifacts of thermodynamical observables disappear at two-loop order, as was already the case for the SU(2) theory. In particular, the entropy and the pressure are positive for all temperatures. Finally, we discuss the groups SU(4) and Sp(2) which shed interesting light, respectively, on the relation between the (de)confinement of static matter sources in the various representations of the gauge group and on the use of the background field itself as an order parameter for confinement. In both cases, we obtain first-order transitions, in agreement with lattice simulations and other continuum approaches.