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.
The lattice infrared Landau gauge gluon propagator: from finite volume to the infinite volume
