Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge

TL;DR

This paper investigates the properties of the Gribov region in SU(N) Yang-Mills theories within the maximal Abelian gauge, analyzing its geometric features and effects on propagators and condensates.

Contribution

It extends the understanding of the Gribov region to SU(N) theories, detailing its properties and the impact of the Gribov restriction on propagators and condensates.

Findings

The Gribov region is convex and bounded along off-diagonal directions.

The restriction influences gluon and ghost propagators.

Dimension two condensates are affected by the Gribov horizon.

Abstract

In this paper we address the issue of the Gribov copies in SU(N), N>2, Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. A few properties of the Gribov region in this gauge are established. Similarly to the case of SU(2), the Gribov region turns out to be convex, bounded along the off-diagonals directions in field space, and unbounded along the diagonal ones. The implementation of the restriction to the Gribov region in the functional integral is discussed through the introduction of the horizon function, whose construction will be outlined in detail. The influence of this restriction on the behavior of the gluon and ghost propagators of the theory is also investigated together with a set of dimension two condensates.