Abelian and center gauges in continuum Yang-Mills-Theory

TL;DR

This paper investigates Abelian and center gauges in continuum Yang-Mills theory, focusing on their ability to detect magnetic monopoles and center vortices, and analyzes specific field configurations like instantons and merons.

Contribution

It introduces Gribov-copy-free Laplacian gauges and studies their effectiveness in identifying topological structures in various gauge field configurations.

Findings

Merons are associated with center vortices.

Single instantons do not produce center vortices.

Instanton-anti-instanton pairs are enclosed by a vortex with monopole loops.

Abstract

Abelian and center gauges are considered in continuum Yang-Mills theory in order to detect the magnetic monopole and center vortex content of gauge field configurations. Specifically we examine the Laplacian Abelian and center gauges, which are free of Gribov copies, as well as the center gauge analog of the (Abelian) Polyakov gauge. In particular, we study meron, instanton and instanton-anti-instanton field configurations in these gauges and determine their monopole and vortex content. While a single instanton does not give rise to a center vortex, we find center vortices for merons. Furthermore we provide evidence, that merons can be interpreted as intersection points of center vortices. For the instanton-anti-instanton pair, we find a center vortex enclosing their centers, which carries two monopole loops.