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

Abstract

In this work, we study the propagators of matter fields within the framework of the refined GribovZwanziger theory, which takes into account the effects of the Gribov copies in the gauge-fixing quantization procedure of Yang-Mills theory. In full analogy with the pure gluon sector of the refined Gribov-Zwanziger action, a non-local long-range term in the inverse of the FaddeevPopov operator is added in the matter sector.

Renormalizability of the refined Gribov-Zwanziger action in linear covariant gauges

“…In the Landau gauge, dealing with Gribov copies has brought non-trivial infrared effects which might be related to the confinement of gluons, see [5,[68][69][70], a fact that has raised the investigation of such effects in other gauges. In particular, the issue of the Gribov copies in the linear covariant gauges has been object of intense research in the last years, see [46,[49][50][51][52][53][54][55]. In particular, a local and BRST invariant action which takes into account the existence of Gribov copies in the linear covariant gauges was proposed in [49], within the Gribov-Zwanziger framework.…”

“…Owing to the aforementioned prescription for a BRST-invariant (R)GZ construction in the linear covariant gauges, it was established in [50] that, in great similarity with the Landau gauge, the formation of the refining condensates happens in d = 3, 4 but not in d = 2. Also, matter fields were introduced in [55] according to the prescription developed in [32], giving rise to analytic expressions for the non-perturbative propagators for scalar fields in the adjoint representation of the gauge group as well as for quarks in the fundamental representation.…”

“…Although this class of gauges preserves the linearity of the Landau gauge, it introduces a gauge parameter α as well as a longitudinal sector for the gluon fields. In a series of papers [46,[49][50][51][52][53][54][55], the development of the RGZ action to linear covariant gauges was worked out. Besides being interesting by its own as a further development of the RGZ framework, recent studies within analytic as well as numerical lattice approaches to non-perturbative Yang-Mills theories started employing the linear covariant gauges [56][57][58][59][60][61].…”

“…In this paper we pursue the study of the RGZ formulation initiated in [46,[49][50][51][52][53][54][55], by addressing the issue of the renormalizability properties of the local and BRST invariant RGZ action in the linear covariant gauges. In particular, we prove, using the algebraic renormalization setup [62], the all orders renormalizability of the RGZ framework in the linear covariant gauge, a topic which was still lacking in our previous studies.…”

The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem

“…Moreover, as expected, it was also confirmed that different gauge invariant operators, with matching quantum numbers, can describe the same state, by looking into their mutual overlaps/mixed propagators. In particular can one also introduce gauge invariant "dressed" operators, see [18] or [19], based on the seminal work of Dirac [20], to describe the spectrum. We will not pursue this avenue here, but the proper renormalization properties of these dressed field configurations can also be studied in the continuum, next to their correlation functions, including the overlap with the here considered operators.…”