Toward background field independence within the Gribov horizon

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 the Becchi-Rouet-Stora-Tyutin (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) GribovZwanziger action. The issue of background dependence and its relation to gauge parameter dependence is discussed in the light of nonperturbative effects driven by the elimination of Gribov copies.

Automated summary

In this paper, we introduce a background gauge for the quantization of Euclidean Yang-Mills theories, which is deformed by the presence of a gauge parameter. This gauge allows us to explicitly investigate the effects of infinitesimal Gribov copies and their impact on the background and gauge parameter dependence. We construct a BRST symmetric action in this gauge, eliminating regular infinitesimal Gribov copies similar to the recently introduced BRST invariant Gribov-Zwanziger action. The issue of background dependence and its relation to gauge parameter dependence is discussed in the context of nonperturbative effects driven by the elimination of Gribov copies.