More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges

TL;DR

This paper investigates the non-perturbative behavior of the gluon propagator in linear covariant gauges across different dimensions using the Refined Gribov-Zwanziger framework, revealing dimension-dependent behaviors and proposing a lattice-compatible functional.

Contribution

It extends the non-perturbative analysis of gluon propagators to linear covariant gauges with a BRST-invariant approach and introduces a new functional for lattice implementation.

Findings

Gluon propagator shows massive behavior in D=3,4

Gluon propagator exhibits scaling in D=2

Framework respects BRST symmetry

Abstract

In this paper, we discuss the gluon propagator in the linear covariant gauges in $D=2,3,4$ Euclidean dimensions. Non-perturbative effects are taken into account via the so-called Refined Gribov-Zwanziger framework. We point out that, as in the Landau and maximal Abelian gauges, for $D=3,4$, the gluon propagator displays a massive (decoupling) behaviour, while for $D=2$, a scaling one emerges. All results are discussed in a setup that respects the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, through a recently introduced non-perturbative BRST transformation. We also propose a minimizing functional that could be used to construct a lattice version of our non-perturbative definition of the linear covariant gauge.