Effect of the Gribov horizon on the Polyakov loop and vice versa

TL;DR

This paper investigates how the Gribov horizon influences the Polyakov loop in finite temperature SU(2) gauge theory, revealing a direct connection between the dynamical Gribov mass and the deconfinement transition.

Contribution

It introduces a method to simultaneously determine the Gribov mass and Polyakov loop at finite temperature, highlighting their interdependence and the impact on deconfinement in SU(2) gauge theory.

Findings

Gribov mass exhibits a cusp at the deconfinement transition temperature.

The Polyakov loop becomes nonzero at the same critical temperature.

Initial results on the critical temperature from the Refined Gribov-Zwanziger approach.

Abstract

We consider finite temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger (GZ) quantization scheme, which entails the introduction of a dynamical mass scale (Gribov mass) directly influencing the Green functions of the theory. Here, we determine simultaneously the Polyakov loop (vacuum expectation value) and Gribov mass in terms of temperature, by minimizing the vacuum energy w.r.t. the Polyakov loop parameter and solving the Gribov gap equation. Inspired by the Casimir energy-style of computation, we illustrate the usage of Zeta function regularization in finite temperature calculations. Our main result is that the Gribov mass directly feels the deconfinement transition, visible from a cusp occurring at the same temperature where the Polyakov loop becomes nonzero. In this exploratory work we mainly restrict ourselves to the original Gribov-Zwanziger quantization procedure in order to illustrate the approach and the potential direct link between the vacuum structure of the theory (dynamical mass scales) and (de)confinement. We also present a first look at the critical temperature obtained from the Refined Gribov-Zwanziger approach. Finally, a particular problem for the pressure at low temperatures is reported.