Infrared-suppressed gluon propagator in 4d Yang-Mills theory in a Landau-like gauge

TL;DR

This study investigates the infrared behavior of the gluon propagator in 4d SU(2) Yang-Mills theory across a gauge interpolation, confirming infrared suppression consistent with confinement scenarios, and compares results with 3d cases.

Contribution

It introduces a gauge interpolating between Landau and Coulomb gauges and demonstrates infrared suppression of the gluon propagator in this framework, supporting confinement theories.

Findings

Infrared suppression observed for small gauge parameter lambda.

Results align with Gribov-Zwanziger confinement scenario.

Similar suppression confirmed in 3d case.

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 lambda equal to 1) and the minimal Coulomb gauge (corresponding to lambda = 0). For small values of lambda we find that the spatially-transverse gluon propagator D^tr(0,|\vec p|), considered as a function of the spatial momenta |\vec 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 lambda -> 0 (complete Coulomb gauge) and its relation to the standard Coulomb gauge (lambda = 0). Our findings are corroborated by similar results in the three-dimensional case, where the infrared suppression is observed for all considered values of lambda.