Gauge copies in the Landau-DeWitt gauge: a background invariant restriction

TL;DR

This paper develops a background invariant Gribov-Zwanziger effective action in the Landau-DeWitt gauge, addressing gauge copies and avoiding issues like spurious Lorentz symmetry breaking, thus improving the gauge's theoretical consistency.

Contribution

It introduces a novel, background invariant Gribov-Zwanziger action that eliminates gauge copies while maintaining explicit background invariance, unlike previous approaches.

Findings

Eliminates infinitesimal background gauge copies.

Maintains explicit background invariance.

Prevents spurious Lorentz symmetry breaking.

Abstract

The Landau background gauge, also known as the Landau-DeWitt gauge, has found renewed interest during the past decade given its usefulness in accessing the confinement-deconfinement transition via the vacuum expectation value of the Polyakov loop, describable via an appropriate background. In this Letter, we revisit this gauge from the viewpoint of it displaying gauge (Gribov) copies. We generalize the Gribov-Zwanziger effective action in a BRST and background invariant way; this action leads to a restriction on the allowed gauge fluctuations, thereby eliminating the infinitesimal background gauge copies. The explicit background invariance of our action is in contrast with earlier attempts to write down and use an effective Gribov-Zwanziger action. It allows to address certain subtleties arising in these earlier works, such as a spontaneous and thus spurious Lorentz symmetry breaking, something which is now averted.