Propagators and topology

TL;DR

This study investigates the relationship between gluon and topological excitations in Yang-Mills theories by analyzing gluon correlation functions in topological backgrounds, revealing qualitative similarities at low momenta.

Contribution

It demonstrates that low-momentum features of gluon propagators are preserved under smearing, supporting the equivalence of gluonic and topological perspectives in Yang-Mills theories.

Findings

Low-momentum propagator features are retained after smearing.

Mid-momentum behavior is significantly altered by smearing.

Results inform the development of functional truncation methods.

Abstract

Two popular perspectives on the non-perturbative domain of Yang-Mills theories are either in terms of the gluons themselves or in terms of collective gluonic excitations, i.e. topological excitations. If both views are correct, then they are only two different representations of the same underlying physics. One possibility to investigate this connection is by the determination of gluon correlation functions in topological background fields, as created by the smearing of lattice configurations. This is performed here for the minimal Landau gauge gluon propagator, ghost propagator, and running coupling, both in momentum and position space for SU(2) Yang-Mills theory. The results show that the salient low-momentum features of the propagators are qualitatively retained under smearing at sufficiently small momenta, in agreement with an equivalence of both perspectives. However, the mid-momentum behavior is significantly affected. These results are also relevant for the construction of truncations in functional methods, as they provide hints on necessary properties to be retained in truncations.