Gribov horizon, Polyakov loop and finite temperature

TL;DR

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

Contribution

It provides a continuum analysis of the deconfinement transition by linking the Gribov horizon effects with the Polyakov loop in SU(2) gauge theory.

Findings

The Gribov mass exhibits a cusp at the deconfinement temperature.

The Polyakov loop becomes nonzero at the same temperature as the cusp.

Issues with pressure calculations at low temperatures are identified.

Abstract

We consider finite-temperature $SU(2)$ gauge theory in the continuum formulation. Choosing the Landau gauge, the existing gauge copies are taken into account by means of the Gribov-Zwanziger 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 with respect to the Polyakov-loop parameter and solving the Gribov gap equation. The 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. Finally, problems for the pressure at low temperatures are reported.