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

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.