On the Faddeev-Popov operator eigenspectrum in topological background fields

TL;DR

This paper analytically investigates the Faddeev-Popov operator's eigenspectrum in topological backgrounds, revealing additional zero-modes in instanton and vortex fields, which may relate to confinement mechanisms in quantum chromodynamics.

Contribution

It provides an analytical study of the Faddeev-Popov operator spectrum in topological backgrounds, linking zero-modes to confinement features.

Findings

Both instanton and vortex backgrounds produce zero-modes in the Faddeev-Popov spectrum.

Vortex configurations satisfy a necessary condition for color confinement.

Results align with lattice gauge theory studies of vortices.

Abstract

During the last years significant progress has been made in the understanding of the confinement of quarks and gluons. However, this progress has been made in two directions, which are at first sight very different. On the one hand, topological configurations seem to play an important role in the formation of the static quark-anti-quark potential. On the other hand, when studying Green's functions, the Faddeev-Popov operator seems to be of importance, especially its spectrum near zero. To investigate whether a connection between both aspects exist, the eigenspectrum of the Faddeev-Popov operator in an instanton and a center-vortex background field are determined analytically in the continuum. It is found that both configurations give rise to additional zero-modes. This agrees with corresponding studies of vortices in lattice gauge theory. In the vortex case also one necessary condition for the confinement of color is fulfilled. Some possible consequences of the results will be discussed, and also a few remarks on monopoles will be given.