Towards background field independence within the Gribov horizon

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.

14 pages

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• The complex heavy-quark potential with the Gribov-Zwanziger action
• Polyakov loop, gluon mass, gluon condensate and its asymmetry near deconfinement
• Heavy quark dynamics via Gribov-Zwanziger approach
• The gap equations of background field invariant Refined Gribov-Zwanziger action proposals and the deconfinement transition