Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory

TL;DR

This paper investigates the non-perturbative infrared behavior of higher-dimensional Yang-Mills theories using the Refined Gribov-Zwanziger framework, revealing a dimension-dependent decoupling solution for the gluon propagator and a novel coupling mechanism upon dimensional reduction.

Contribution

It extends the Gribov-Zwanziger approach to higher dimensions and uncovers a new coupling mechanism from dimensional reduction, advancing understanding of gauge copies and infrared dynamics.

Findings

Evidence for a decoupling/massive gluon propagator in higher dimensions

The decoupling behavior becomes more pronounced with increasing dimension

Identification of a non-perturbative coupling arising from dimensional reduction

Abstract

In this paper, we discuss non-perturbative infrared features of Yang-Mills theory in Euclidean space-time dimensions greater than four in the Landau gauge and within the Refined Gribov-Zwanziger framework, which enables us to take into account the existence of gauge copies by restricting the domain of integration in the path integral to the Gribov region. Evidences for a decoupling/massive solution for the gluon propagator in higher dimensions are provided. This behavior is strengthened the bigger the dimension is. Further, we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action from five to four dimensions, a non-perturbative coupling between the inverse of the Faddeev-Popov operator and the scalar field corresponding to the fifth component of the gauge field naturally arises, being in agreement with the recently proposed mechanism \cite{Capri:2014bsa} to generalize the Refined Gribov-Zwanziger construction to the matter sector.