More on Gribov copies and propagators in Landau-gauge Yang-Mills theory

TL;DR

This paper investigates how different non-perturbative gauge fixing methods, specifically the minimal and absolute Landau gauges, affect gluon and ghost propagators in SU(2) Yang-Mills theory, revealing significant differences in the infrared regime.

Contribution

It provides a detailed numerical comparison of propagators in different Landau gauges, highlighting the impact of Gribov copies on non-perturbative gauge-dependent correlation functions.

Findings

Propagators differ significantly in the infrared region.

Finite-volume effects are altered between gauges.

Differences are observed in both 2D and 3D cases.

Abstract

Fixing a gauge in the non-perturbative domain of Yang-Mills theory is a non-trivial problem due to the presence of Gribov copies. In particular, there are different gauges in the non-perturbative regime which all correspond to the same definition of a gauge in the perturbative domain. Gauge-dependent correlation functions may differ in these gauges. Two such gauges are the minimal and absolute Landau gauge, both corresponding to the perturbative Landau gauge. These, and their numerical implementation, are described and presented in detail. Other choices will also be discussed. This investigation is performed, using numerical lattice gauge theory calculations, by comparing the propagators of gluons and ghosts for the minimal Landau gauge and the absolute Landau gauge in SU(2) Yang-Mills theory. It is found that the propagators are different in the far infrared and even at energy scales of the order of half a GeV. In particular, also the finite-volume effects are modified. This is observed in two and three dimensions. Some remarks on the four-dimensional case are provided as well.