A local and BRST-invariant Yang-Mills theory within the Gribov horizon

TL;DR

This paper develops a local, BRST-invariant formulation of Yang-Mills theories within the Gribov horizon, enabling precise predictions for gluon propagators and gauge-parameter independence of correlation functions.

Contribution

It introduces a local, BRST-invariant approach to Yang-Mills theories that incorporates Gribov copies using auxiliary fields, advancing the theoretical framework.

Findings

Exact prediction for the longitudinal gluon propagator

Gauge-parameter independence of BRST-invariant correlators

Compatibility with lattice results

Abstract

We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies \`a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.