SU(2) Running Coupling Constant and Confinement in Minimal Coulomb and Landau Gauges

TL;DR

This paper numerically investigates the gluon and ghost propagators in SU(2) gauge theory within Coulomb and Landau gauges, providing insights into the non-perturbative running coupling and confinement mechanisms.

Contribution

It offers the first non-perturbative evaluation of the running coupling and tests Gribov's confinement scenarios in these gauges using lattice simulations.

Findings

Numerical results support Gribov's confinement scenario.

The running coupling exhibits specific behavior consistent with confinement.

Finite-volume effects are carefully analyzed and extrapolated.

Abstract

We present a numerical study of the space-space and time-time components of the gluon propagator at equal time in the minimal Coulomb gauge, and of the gluon and ghost propagators in the minimal Landau gauge. This work allows a non-perturbative evaluation of the running coupling constant and a numerical check of Gribov's confinement scenarios for these two gauges. Our simulations are done in pure SU(2) lattice gauge theory at $\beta = 2.2$. We consider several lattice volumes in order to control finite-volume effects and extrapolate our results to infinite lattice volume.