Monopoles, abelian projection, and gauge invariance

TL;DR

This paper establishes a gauge-invariant connection between non-Abelian Bianchi identities and abelian monopoles, demonstrating that monopole condensation is a physical, gauge-invariant phenomenon independent of the abelian projection used.

Contribution

It proves a direct link between NABI violations and magnetic currents, showing monopole condensation is gauge-invariant and identifying the maximal-abelian gauge as a valid choice.

Findings

Magnetic current violation is gauge-invariant.

Not all abelian projections reveal monopoles.

Monopole condensation is a gauge-invariant phenomenon.

Abstract

A direct connection is proved between the Non-Abelian Bianchi Identities(NABI), and the abelian Bianchi identities for the 't Hooft tensor. As a consequence the existence of a non-zero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows to show that not all abelian projections can be used to expose monopoles in lattice configurations: each field configuration with non-zero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-abelian gauge is a legitimate choice. It is also proved, starting from the NABI, that monopole condensation is a physical gauge invariant phenomenon, independent of the choice of the abelian projection.