A Gribov-Zwanziger type action invariant under background gauge transformations

TL;DR

This paper introduces a background gauge invariant Gribov-Zwanziger action for Yang-Mills theories, analyzing its implications for the deconfinement transition at one-loop level and exploring the role of color-dependent Gribov parameters.

Contribution

It develops a background gauge invariant Gribov-Zwanziger action applicable to any gauge group, extending previous models and analyzing the deconfinement transition with novel color-dependent parameters.

Findings

Model relates to Gribov no-pole condition at zero temperature.

Color-dependent Gribov parameters can be negative without losing potential reality.

Analysis of deconfinement transition requires resolving the potential in certain regions.

Abstract

We propose a Gribov-Zwanziger type action for the Landau-DeWitt gauge that preserves, for any gauge group, the invariance under background gauge transformations. At zero temperature, and to one-loop accuracy, the model can be related to the Gribov no-pole condition. We apply the model to the deconfinement transition in SU(2) and SU(3) Yang-Mills theories and compare the predictions obtained with a single or with various (color dependent) Gribov parameters that can be introduced in the action without jeopardizing its background gauge invariance. The Gribov parameters associated to color directions orthogonal to the background can become negative, while keeping the background effective potential real. In some cases, the proper analysis of the transition requires the potential to be resolved in those regions.