We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.

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

In this paper, we discuss the gluon propagator in the linear covariant gauges in D = 2, 3, 4 Euclidean dimensions. Nonperturbative effects are taken into account via the so-called refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for D = 3, 4, the gluon propagator displays a massive (decoupling) behavior, while for D = 2, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced nonperturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our nonperturbative definition of the linear covariant gauge

The Refined Gribov-Zwanziger framework takes into account the existence of equivalent gauge field configurations in the gauge-fixing quantization procedure of Euclidean Yang-Mills theories. Recently, this setup was extended to the family of linear covariant gauges giving rise to a local and BRST-invariant action. In this paper, we give an algebraic proof of the renormalizability of the resulting action to all orders in perturbation theory. CONTENTS

We address the issue of the renormalizability of the gauge-invariant non-local dimensiontwo operator A 2 min , whose minimization is defined along the gauge orbit. Despite its non-local character, we show that the operator A 2 min can be cast in local form through the introduction of an auxiliary Stueckelberg field. The localization procedure gives rise to an unconventional kind of Stueckelberg-type action which turns out to be renormalizable to all orders of perturbation theory. In particular, as a consequence of its gauge invariance, the anomalous dimension of the operator A 2 min turns out to be independent from the gauge parameter α entering the gauge-fixing condition, being thus given by the anomalous dimension of the operator A 2 in the Landau