Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

TL;DR

This study investigates the impact of the Gribov ambiguity on the ghost and gluon propagators in lattice SU(2) Landau gauge Yang-Mills theory at strong coupling, highlighting the ambiguity's significant effect on the ghost propagator.

Contribution

It provides a detailed analysis of the Gribov ambiguity's effects at infinite lattice spacing, emphasizing its severity for the ghost propagator in lattice gauge theory.

Findings

Gribov ambiguity greatly affects the ghost propagator

Gluon propagator is only mildly influenced by the Gribov problem

Results suggest need for refined studies at finite coupling

Abstract

We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite beta. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.