Properties of the Faddeev-Popov operator in the Landau gauge, matter confinement and soft BRST breaking

TL;DR

This paper explores the non-perturbative properties of the Faddeev-Popov operator in Landau gauge, linking matter confinement and soft BRST breaking, and proposes a framework consistent with lattice data.

Contribution

It introduces a local, renormalizable framework that captures soft BRST breaking effects in matter sectors and predicts non-perturbative propagators aligned with lattice results.

Findings

Proposes a signature for BRST breaking in matter sectors.

Constructs a framework consistent with lattice data.

Predicts non-perturbative matter propagators.

Abstract

In light of the development of the Gribov issue for pure Euclidean gauge theories and of the recent lattice measurement of soft breaking of the BRST invariance in Yang-Mills theories in the Landau gauge, we consider non-perturbative features in the gauge-interacting matter sector and their relation with general properties of the Faddeev-Popov operator. A signature for BRST breaking in the matter sector is proposed and a local and renormalizable framework is constructed, accommodating this signature and predicting non-perturbative matter propagators that are consistent with available lattice data for adjoint scalars and quarks.