Scaling Properties of the Probability Distribution of Lattice Gribov Copies

TL;DR

This paper investigates how the probability of finding Gribov copies in lattice gauge fixing increases with lattice size and examines their impact on Green functions, revealing volume-dependent effects and equivalence of certain gauge copies.

Contribution

It demonstrates the volume dependence of Gribov copy occurrence and their influence on Green functions, providing insights into gauge fixing ambiguities in lattice SU(2) gauge theory.

Findings

Probability of Gribov copies increases with lattice size beyond a critical volume.

Ghost propagator depends on the choice of Gribov copy, with dependence decreasing at larger volumes.

Gluon propagator and three-point functions are insensitive to Gribov copy choice within errors.

Abstract

We study the problem of the Landau gauge fixing in the case of the SU(2) lattice gauge theory. We show that the probability to find a lattice Gribov copy increases considerably when the physical size of the lattice exceeds some critical value $\approx2.75/\sqrt{\sigma}$, almost independent of the lattice spacing. The impact of the choice of the copy on Green functions is presented. We confirm that the ghost propagator depends on the choice of the copy, this dependence decreasing for increasing volumes above the critical one. The gluon propagator as well as the gluonic three-point functions are insensitive to choice of the copy (within present statistical errors). Finally we show that gauge copies which have the same value of the minimisation functional ($\int d^4x (A^a_\mu)^2$) are equivalent, up to a global gauge transformation, and yield the same Green functions.