Effective models of a semi-quark gluon plasma

TL;DR

This paper investigates models of a semi-quark gluon plasma, focusing on how to generate the second Bernoulli polynomial dynamically and analyzing the behavior of free energy near zero holonomy using different methods.

Contribution

It compares two methods for generating the second Bernoulli polynomial and finds that only the two-dimensional ghost approach yields a well-behaved free energy as holonomy approaches zero.

Findings

The ghost method produces a continuous free energy at zero holonomy.

The auxiliary field method results in a discontinuous free energy at zero holonomy.

The study clarifies the behavior of the free energy in semi-quark gluon plasma models.

Abstract

In the deconfined regime of a non-Abelian gauge theory at nonzero temperature, previously it was argued that if a (gauge invariant) source is added to generate nonzero holonomy, that this source must be linear for small holonomy. The simplest example of this is the second Bernoulli polynomial. However, then there is a conundrum in computing the free energy to $\sim g^3$ in the coupling constant $g$, as part of the free energy is discontinuous as the holonomy vanishes. In this paper we investigate two ways of generating the second Bernoulli polynomial dynamically: as a mass derivative of an auxiliary field, and from two dimensional ghosts embedded isotropically in four dimensions. Computing the holonomous hard thermal loop (HHTL) in the gluon self-energy, we find that the limit of small holonomy is only well behaved for two dimensional ghosts, with a free energy which to $\sim g^3$ is continuous as the holonomy vanishes.