Two-loop perturbative corrections to the thermal effective potential in gluodynamics

TL;DR

This paper calculates two-loop perturbative corrections to the effective potential in pure gluodynamics, revealing a proportionality to the one-loop action across various gauge groups, simplifying the understanding of the thermodynamics of gluon fields.

Contribution

It provides a novel, simplified expression for two-loop corrections to the Polyakov loop effective action, applicable to all classical and exceptional gauge groups.

Findings

Two-loop corrections are proportional to the one-loop action.

The result is independent of the eigenvalues of the Polyakov loop.

The proportionality holds for all classical and exceptional groups.

Abstract

The thermodynamics of pure glue theories can be described in terms of an effective action for the Polyakov loop. This effective action is of the Landau-Ginzburg type and its variables are the angles parametrizing the loop. In this paper we compute perturbative corrections to this action. Remarkably, two-loop corrections turn out to be proportional to the one-loop action, independent of the eigenvalues of the loop. By a straightforward generalization of the 't Hooft coupling this surprisingly simple result holds for any of the classical and exceptional groups.