We prove the renormalizability to all orders of a refined Gribov-Zwanziger type action in linear covariant gauges in four-dimensional Euclidean space. In this model, the Gribov copies are taken into account by requiring that the Faddeev-Popov operator is positive definite with respect to the transverse component of the gauge field, a procedure which turns out to be analogous to the restriction to the Gribov region in the Landau gauge. The model studied here can be regarded as the first approximation of a more general nonperturbative BRST invariant formulation of the refined Gribov-Zwanziger action in linear covariant gauges obtained recently in [1,2]. A key ingredient of the set up worked out in [1,2] is the introduction of a gauge invariant field configuration A µ which can be expressed as an infinite non-local series in the starting gauge field A µ . In the present case, we consider the approximation in which only the first term of the series representing A µ is considered, corresponding to a pure transverse gauge field. The all order renormalizability of the resulting action gives thus a strong evidence of the renormalizability of the aforementioned more general nonperturbative BRST invariant formulation of the Gribov horizon in linear covariant gauges.

The dimension two gauge invariant non-local operator A 2 min , obtained through the minimization of d 4 xA 2 along the gauge orbit, allows to introduce a non-local gauge invariant configuration A h µ which can be employed to built up a class of Euclidean massive Yang-Mills models useful to investigate non-perturbative infrared effects of confining theories. A fully local setup for both A 2 min and A h µ can be achieved, resulting in a local and BRST invariant action which shares similarities with the Stueckelberg formalism. Though, unlike the case of the Stueckelberg action, the use of A 2 min gives rise to an all orders renormalizable action, a feature which will be illustrated by means of a class of covariant gauge fixings which, as much as 't Hooft's R ζ -gauge of spontaneously broken gauge theories, provide a mass for the Stueckelberg field. *

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

We construct a vector gauge invariant transverse field configuration V H , consisting of the well-known superfield V and of a Stueckelberg-like chiral superfield. The renormalizability of the Super Yang Mills action in the Landau gauge is analyzed in the presence of a gauge invariant mass term m 2 dV M(V H), with M(V H) a power series in V H. Unlike the original Stueckelberg action, the resulting action turns out to be renormalizable to all orders.