INFRARED-SUPPRESSED GLUON PROPAGATOR IN 4D YANG–MILLS THEORY IN A LANDAU-LIKE GAUGE

Abstract

The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov–Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge parameter λ equal to 1) and the minimal Coulomb gauge (corresponding to λ = 0). For small values of λ we find that the spatially-transverse gluon propagator D tr (0, |p|), considered as a function of the spatial momenta |p|, is clearly infrared suppressed. This result is in agreement with the Gribov–Zwanziger scenario and with previous numerical results in the minimal Coulomb gauge. We also discuss the nature of the limit λ→0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (λ = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of λ.