Instantons, monopoles, vortices, and the Faddeev-Popov operator eigenspectrum

TL;DR

This paper explores how topological configurations like instantons, monopoles, and vortices influence the Faddeev-Popov operator's spectrum, revealing their potential role in the confinement mechanism within quantum field theory.

Contribution

It demonstrates that topological configurations contribute similarly to the Faddeev-Popov operator's spectrum, supporting a connection between different confinement scenarios.

Findings

Topological configurations add zero-modes to the spectrum.

Instantons, monopoles, and vortices similarly affect the spectrum.

These configurations may all contribute to the confinement mechanism.

Abstract

The relation of confinement scenarios based on topological configurations and the Gribov-Zwanziger scenario is examined. To this end the eigenspectrum of the central operator in the Gribov-Zwanziger scenario, the Faddeev-Popov operator, is studied in topological field configurations. It is found that instantons, monopoles, and vortices contribute to the spectrum in a qualitatively similar way. Especially, all give rise to additional zero-modes and thus can contribute to the Gribov-Zwanziger confinement mechanism. Hence a close relation between these confinement scenarios likely exists.