Exact nilpotent nonperturbative BRST symmetry for the Gribov-Zwanziger action in the linear covariant gauge

Abstract

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.

A non-perturbative study of matter field propagators in Euclidean Yang–Mills theory in linear covariant, Curci–Ferrari and maximal Abelian gauges

“…In this section, we review the recently proposed BRSTinvariant formulation of the refined Gribov-Zwanziger action in linear covariant [1,3], Curci-Ferrari [4] and maximal Abelian gauges [54]. For the benefit of the reader, we start with a brief overview of the Gribov problem in the Landau gauge for which the refined Gribov-Zwanziger action was originally constructed.…”

“…However, the soft breaking of the BRST symmetry in the (refined) Gribov-Zwanziger setup gives rise to non-trivial complications for such a task. Nevertheless, recently, in [1], a reformulation of the Gribov-Zwanziger action in the Landau gauge in terms of a transverse and gauge-invariant field, 4 see [66][67][68], A h,a μ , with ∂ μ A h,a μ = 0, and its generalization to linear covariant gauges was proposed. In this new formulation, the Gribov-Zwanziger enjoys an exact nilpotent BRST symmetry, which is a direct consequence of the gauge invariance of A h,a μ and which enables us to establish the independence from the parameter α of the gauge-invariant correlation functions, and this even in the presence of the Gribov horizon.…”

“…Upon a suitable redefinition of the field b a , b a → b h,a [1], with the introduction of the gauge-invariant field A h,a μ , the resulting Gribov-Zwanziger action in linear covariant gauges is written as [1] …”

“…Very recently, the refined Gribov-Zwanziger framework has been extended to the class of the linear covariant and Curci-Ferrari gauges [1][2][3][4][5], allowing, in particular, to establish the independence from the gauge parameter of the gaugeinvariant correlation functions as well of the poles of the transverse part of the gluon propagator. In the light of such developments, it seems natural to ask ourselves how matter fields should be coupled to the refined Gribov-Zwanziger action in such gauges.…”

Analytic structure of QCD propagators in Minkowski space

“…Important insights also come from physically motivated phenomenological models, providing simplified analytical descriptions that can be easily continued to Minkowski space [35][36][37][38][39][40][41][42]. For instance, the existence of complex poles was predicted by the refined version [42][43][44] of the Gribov-Zwanziger model [45].…”