Covariant gauges without Gribov ambiguities in Yang-Mills theories

TL;DR

This paper introduces a new family of nonlinear covariant gauges for Yang-Mills theories that are free of Gribov ambiguities, potentially improving gauge fixing and calculations of correlators.

Contribution

It proposes a Gribov-ambiguity-free gauge fixing method with a local action, suitable for lattice implementation, and demonstrates its renormalizability in four dimensions.

Findings

Reduces to known gauges at high energies

Provides explicit one-loop renormalization factors

Potentially improves Yang-Mills correlator calculations

Abstract

We propose a one-parameter family of nonlinear covariant gauges which can be formulated as an extremization procedure that may be amenable to lattice implementation. At high energies, where the Gribov ambiguities can be ignored, this reduces to the Curci-Ferrari-Delbourgo-Jarvis gauges. We further propose a continuum formulation in terms of a local action which is free of Gribov ambiguities and avoids the Neuberger zero problem of the standard Faddeev-Popov construction. This involves an averaging over Gribov copies with a nonuniform weight, which introduces a new gauge-fixing parameter. We show that the proposed gauge-fixed action is perturbatively renormalizable in four dimensions and we provide explicit expressions of the renormalization factors at one loop. We discuss the possible implications of the present proposal for the calculation of Yang-Mills correlators.