Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge

TL;DR

This paper extends the non-perturbative BRST symmetry framework from the Landau gauge to the maximal Abelian gauge in Euclidean Yang-Mills theories, analyzing the resulting gluon propagator behaviors across different dimensions.

Contribution

It generalizes the non-perturbative BRST symmetry to the maximal Abelian gauge and evaluates the diagonal gluon propagator in various dimensions.

Findings

Decoupling behavior in D=4,3 dimensions.

Scaling behavior in D=2 dimension.

Extension of BRST symmetry to new gauge setting.

Abstract

The non-perturbative nilpotent exact BRST symmetry of the Gribov-Zwanziger action in the Landau gauge constructed in [ arXiv:1506.06995 [hep-th]] is generalized to the case of Euclidean Yang-Mills theories quantized in the maximal Abelian gauge. The resulting diagonal gluon propagator is evaluating in dimensions D=4,3,2. In D=4,3 a decoupling type behavior is found in the infrared region, while in D=2 a scaling type behavior emerges.