The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories

TL;DR

This paper demonstrates that Zwanziger's horizon function maintains a universal, gauge-independent character across various covariant gauges in Euclidean Yang-Mills theories, ensuring consistent physical correlators.

Contribution

It establishes the gauge invariance of the horizon function's correlation functions within a BRST invariant framework for Yang-Mills theories.

Findings

Correlation functions are gauge parameter independent.

Results reduce to Landau gauge when parameters are zero.

Gauge invariance of the Gribov region restriction is confirmed.

Abstract

In light of the recently established BRST invariant formulation of the Gribov-Zwanziger theory, we show that Zwanziger's horizon function displays a universal character. More precisely, the correlation functions of local BRST invariant operators evaluated with the Yang-Mills action supplemented with a BRST invariant version of the Zwanziger's horizon function and quantized in an arbitrary class of covariant, color invariant and renormalizable gauges which reduce to the Landau gauge when all gauge parameters are set to zero, have a unique, gauge parameters independent result, corresponding to that of the Landau gauge when the restriction to the Gribov region $\Omega$ in the latter gauge is imposed. As such, thanks to the BRST invariance, the cut-off at the Gribov region $\Omega$ acquires a gauge independent meaning in the class of the physical correlators.