Non-perturbative analysis of the Gribov-Zwanziger action

TL;DR

This paper provides a non-perturbative infrared analysis of the Gribov-Zwanziger action, confirming that only one scaling solution aligns with the Faddeev-Popov results, emphasizing boundary conditions over measure restrictions.

Contribution

It explicitly analyzes the infrared behavior of the Gribov-Zwanziger action, demonstrating the uniqueness of the scaling solution consistent with Faddeev-Popov results.

Findings

Only one infrared scaling solution remains.

The ghost propagator is infrared enhanced.

The gluon propagator is infrared suppressed.

Abstract

In the non-perturbative regime the usual gauge fixing is not sufficient due to the Gribov problem. To deal with it one can restrict the integration in the path integral to the first Gribov region by using the Gribov-Zwanziger action. In its local form it features additional auxiliary fields which mix with the gluon at the two-point level. We present an explicit infrared analysis of this action. We show that from the two possible scaling solutions obtained previously only one remains: It coincides exactly with the results from the Faddeev-Popov action, i.e., the ghost propagator is infrared enhanced and the gluon propagator infrared suppressed and the corresponding power law behavior is described by only one parameter kappa=0.5953. This corroborates the argument by Zwanziger that for functional equations it suffices to take into account the appropriate boundary conditions and no explicit restriction in the path integral measure is required.