Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement

TL;DR

This paper develops a BRST invariant model linking gluon condensates to deconfinement phase transitions in Yang-Mills theories, providing insights into the nature and temperature of these transitions.

Contribution

It introduces a BRST invariant generalization of the massive background Landau gauge that incorporates a gluon condensate as a dynamically generated mass parameter, and analyzes deconfinement transitions.

Findings

Continuous transition at Tc ~ 0.230 GeV for SU(2)

First order transition at Tc ~ 0.164 GeV for SU(3)

Model results closely match previous Curci-Ferrari approach

Abstract

We consider a BRST invariant generalization of the "massive background Landau gauge", resembling the original Curci-Ferrari model that saw a revived interest due to its phenomenological success in modeling infrared Yang-Mills dynamics, including that of the phase transition. Unlike the Curci-Ferrari model, however, the mass parameter is no longer a phenomenological input but it enters as a result of dimensional transmutation via a BRST invariant dimension two gluon condensate. The associated renormalization constant is dealt with using Zimmermann's reduction of constants program which fixes the value of the mass parameter to values close to those obtained within the Curci-Ferrari approach. Using a self-consistent background field, we can include the Polyakov loop and probe the deconfinement transition, including its interplay with the condensate and its electric-magnetic asymmetry. We report a continuous phase transition at Tc ~ 0.230 GeV in the SU(2) case and a first order one at Tc ~ 0.164 GeV in the SU(3) case, values which are again rather close to those obtained within the Curci-Ferrari model at one-loop order.