Renormalizability of the linearly broken formulation of the BRST symmetry in presence of the Gribov horizon in Landau gauge Euclidean Yang-Mills theories

TL;DR

This paper demonstrates that the linearly broken BRST symmetry in Landau gauge Euclidean Yang-Mills theories with the Gribov horizon remains renormalizable to all orders, ensuring consistency of the Gribov-Zwanziger framework.

Contribution

It proves the all-order multiplicative renormalizability of the linearly broken BRST formulation in Gribov-Zwanziger theories, preserving key non-renormalization properties.

Findings

Renormalizability of the theory is guaranteed by Slavnov-Taylor identities.

The non-renormalization theorem of the gluon-ghost-antighost vertex is established.

Only two renormalization factors are needed for the theory.

Abstract

In previous work arXiv:1009.4135 we have shown that the soft breaking of the BRST symmetry arising within the Gribov-Zwanziger framework can be converted into a linear breaking, while preserving the nilpotency of the BRST operator. Due to its compatibility with the Quantum Action Principle, the linearly broken BRST symmetry directly translates into a set of Slavnov-Taylor identities. We show that these identities guarantee the multiplicative renormalizability of both Gribov-Zwanziger and Refined Gribov-Zwanziger theories to all orders. The known property that only two renormalization factors are needed is recovered. The non-renormalization theorem of the gluon-ghost-antighost vertex as well as the renormalization factor of the Gribov parameter are derived within the linearly broken formulation.