Gribov ambiguities in the maximal Abelian gauge

TL;DR

This paper studies how Gribov copies affect gluon and ghost propagators in SU(2) Yang-Mills theory within the maximal Abelian gauge, revealing characteristic behaviors and comparing with lattice data.

Contribution

It extends Gribov's approach to the maximal Abelian gauge, analyzing the impact on propagators and incorporating the dimension two gluon condensate.

Findings

Diagonal gluon propagator shows Gribov behavior

Off-diagonal gluon has Yukawa type with dynamical mass

Off-diagonal ghost exhibits infrared enhancement

Abstract

The effects of the Gribov copies on the gluon and ghost propagators are investigated in SU(2) Euclidean Yang-Mills theory quantized in the maximal Abelian gauge. By following Gribov's original approach, extended to the maximal Abelian gauge, we are able to show that the diagonal component of the gluon propagator displays the characteristic Gribov type behavior. The off-diagonal component is found to be of the Yukawa type, with a dynamical mass originating from the dimension two gluon condensate, which is also taken into account. Furthermore, the off-diagonal ghost propagator exhibits infrared enhancement. Finally, we make a comparison with available lattice data.