Coulomb gauge studies of SU(3) Yang-Mills theory on the lattice

TL;DR

This study investigates the infrared properties of SU(3) Yang-Mills theory in Coulomb gauge on the lattice, focusing on the ghost propagator, Coulomb potential, and gluon propagators, addressing Gribov issues and finite size effects.

Contribution

It provides new lattice results on the infrared behavior of Yang-Mills theory in Coulomb gauge, highlighting the impact of Gribov copies and improved gauge fixing methods.

Findings

Ghost propagator is infrared enhanced.

Coulomb potential extends to lower momenta and shows complex infrared behavior.

Coulomb string tension satisfies Zwanziger's inequality, with systematic Gribov effects noted.

Abstract

We study the infrared behaviour of lattice SU(3) Yang-Mills theory in Coulomb gauge in terms of the ghost propagator, the Coulomb potential and the transversal and the time-time component of the equal-time gluon propagator. In particular, we focus on the Gribov problem and its impact on the observables. We observe that the simulated annealing method is advantageous for fixing the Coulomb gauge in large volumes. We study finite size and discretization effects. While finite size effects can be controlled by the cone cut, and the ghost propagator and the Coulomb potential become scaling functions with the cylinder cut, the equal-time gluon propagator does not show scaling in the considered range of the inverse coupling constant. The ghost propagator is infrared enhanced. The Coulomb potential is now extended to considerably lower momenta and shows a more complicated infrared regime. The Coulomb string tension satisfies Zwanziger's inequality, but its estimate can be considered only preliminary because of the systematic Gribov effect that is particularly strong for the Coulomb potential.