Non-perturbative BRST quantization of Euclidean Yang–Mills theories in Curci–Ferrari gauges

Abstract

In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a Refined Gribov-Zwanziger action for this gauge which takes into account the presence of gauge copies as well as the dynamical formation of dimension two condensates. This action enjoys a nonperturbative BRST symmetry recently proposed in [1]. Finally, we give attention to the gluon propagator in different space-time dimensions.A fundamental task in theoretical physics is the understanding of non-perturbative aspects of Yang-Mills theories due to the confinement of quarks and gluons, see [2] for a general and updated overview. In this regime, the standard well developed perturbation theory is not meaningful and different techniques must be invoked. So far, we have a good toolbox to access the strongly coupled regime with different approaches as lattice simulations, Dyson-Schwinger equations, functional renormalization group methods, holographic techniques, effective models and others, see [2,3]. Despite the impressive progress achieved in the last decade, it seems fair to state that many aspects of the confinement are still to be unraveled.A long standing problem in the quantization of Yang-Mills theories is the presence of Gribov/gauge copies after the imposition of the gauge fixing condition * [4]. Within the Faddeev-Popov quantization procedure, these spurious configurations are still being taken into account in * aduarte@if.uff.br †

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

“…This was achieved by the introduction of the suitable gauge-invariant fields A h , φ h and ψ h , see [1][2][3][4][5], which, albeit local, are non-polynomial in the auxiliary Stueckelberg-type field ξ a . Nevertheless, such variables as well as the proposed non-perturbative matter coupling give rise to a local ation which can be proven to be renormalizable to all orders, see [70,81].…”

“…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.…”

“…In [4], it was argued that the Gribov problem in the CurciFerrari gauge is intimately related to the existence of copies in the linear covariant gauges. By a suitable shift of the bfield, it was shown that the copies equation is the same in both gauges.…”

“…As such, the issue of the Gribov copies can be handled in the same way and the implementation of the restriction of the domain of integration in the path integral is obtained by the introduction of the same horizon function (22). As discussed in [4], the Gribov-Zwanziger action in the Curci-Ferrari gauge is…”

“…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.…”