Towards background field independence within the Gribov horizon

TL;DR

This paper develops a background gauge for Euclidean Yang-Mills theories that incorporates a gauge parameter, enabling the study of Gribov copies and their influence on physical correlators while maintaining BRST symmetry.

Contribution

It introduces a new background gauge with a gauge parameter, constructs a BRST symmetric action to eliminate Gribov copies, and analyzes background and gauge parameter dependence in non-perturbative regimes.

Findings

Elimination of regular infinitesimal Gribov copies in the new gauge.

Restoration of BRST symmetry with gauge-invariant dressed fields.

Insights into background and gauge parameter dependence related to Gribov horizon effects.

Abstract

We introduce a background gauge akin to the Landau-DeWitt gauge but deformed by the presence of a gauge parameter for the quantization of Euclidean Yang-Mills theories. In the limit where the background field vanishes, standard linear covariant gauges are recovered. This gauge allows for an explicit investigation of the effects of infinitesimal Gribov copies and their impact to background and gauge parameter dependence of physical correlators. Similarly to linear covariant gauges, the introduction of gauge-invariant dressed fields is essential to restore BRST symmetry. Hence, we construct a BRST symmetric action in linear covariant background gauges which eliminates regular infinitesimal Gribov copies in analogy to the recently introduced BRST invariant (refined) Gribov-Zwanziger action. The issue of background dependence and its relation to gauge parameter dependence is discussed in the light of non-perturbative effects driven by the elimination of Gribov copies.