Local and BRST-invariant Yang-Mills theory within the Gribov horizon

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

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

“…However, unlike the Gribov region , a practical way to implement the restriction of the domain of integration in the functional integral to the Fundamental Modular Region has not yet been achieved so far. Therefore, we stick to the Gribov region , which displays important properties: (i) it is bounded in all directions in field space; (ii) it is convex; (iii) all gauge orbits 2 A gauge orbit of a given configuration A a μ is the set of all gauge fields related to A a μ by a gauge transformation.…”

“…As far as the refined Gribov-Zwanziger framewrok is concerned, a possible mechanism to take into account matter confinement was proposed in [2,[24][25][26] in the Landau gauge. More precisely, as will be reviewed in Sect.…”

“…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.…”

“…The proposal made in [2,[24][25][26] consists in generalizing the introduction of the non-local horizon function to the matter sector, in complete analogy with the gluon sector. Moreover, as in the gluon sector, the non-local matter coupling term can be cast in local form, giving rise to a fully local and renormalizable action.…”

“…Moreover, as in the gluon sector, the non-local matter coupling term can be cast in local form, giving rise to a fully local and renormalizable action. In [2,[24][25][26], this prescription was implemented for scalar fields in the adjoint representation of the gauge group and for spinor fields in the fundamental representation. The whole procedure was carried out in the Landau gauge, for which the refined Gribov-Zwanziger setup was well established, see also [54] and the references therein for the maximal Abelian gauge.…”