An effective gluon potential and hybrid approach to Yang-Mills thermodynamics

TL;DR

This paper derives a gluon potential for SU(3) Yang-Mills theory, revealing its limitations at low temperatures and proposing a hybrid model incorporating glueballs to improve thermodynamic descriptions.

Contribution

It introduces a novel effective gluon potential based on the background field method and develops a hybrid approach combining gluons and glueballs for better thermodynamic modeling.

Findings

Gluon contributions are characterized solely by the Polyakov loop.

The derived potential is valid at high temperatures but fails at low temperatures.

A hybrid model with glueballs improves thermodynamic predictions.

Abstract

We derive the partition function for the SU(3) Yang-Mills theory in the presence of a uniform gluon field within the background field method. We show, that the $n$-body gluon contributions in the partition function are characterized solely by the Polyakov loop. We express the effective action through characters of different representations of the color gauge group resulting in a form deduced in the strong-coupling expansion. A striking feature of this potential is that at low temperature gluons are physically disfavored and therefore they do not yield the correct thermodynamics. We suggest a hybrid approach to Yang-Mills thermodynamics, combining the effective gluon potential with glueballs implemented as dilaton fields.