Effective gluon potential and Yang-Mills thermodynamics

TL;DR

This paper derives a thermodynamic potential for pure SU(3) Yang-Mills theory using a perturbative approach, connecting high-temperature behavior with low-temperature confinement via a hybrid model involving glueballs.

Contribution

It introduces a new derivation of the Polyakov-loop potential in perturbation theory and combines it with a glueball-based model to describe Yang-Mills thermodynamics across phases.

Findings

Potential exhibits correct high-temperature asymptotics.

Disfavors gluons at low temperature, consistent with confinement.

Hybrid model matches lattice QCD results in confined phase.

Abstract

We derive the Polyakov-loop thermodynamic potential in the perturbative approach to pure SU(3) Yang-Mills theory. The potential expressed in terms of the Polyakov loop in the fundamental representation corresponds to that of the strong-coupling expansion, of which the relevant coefficients of the gluon energy distribution are specified by characters of the SU(3) group. At high temperature, the potential exhibits the correct asymptotic behavior, whereas at low temperature, it disfavors gluons as appropriate dynamical degrees of freedom. To quantify the Yang-Mills thermodynamics in confined phase, we introduce a hybrid approach which matches the effective gluon potential to that of glueballs, constrained by the QCD trace anomaly in terms of dilaton fields.