Non abelian Bianchi identities, monopoles and gauge invariance

TL;DR

The paper establishes a link between Non-Abelian and Abelian Bianchi identities, showing how gauge choices affect monopole detection on the lattice, but monopole condensation remains gauge invariant.

Contribution

It demonstrates the relation between NABI violations and magnetic currents, clarifies gauge dependence in monopole detection, and confirms gauge invariance of monopole condensation.

Findings

Maximal Abelian Gauge effectively detects monopoles

Landau gauge is not suitable for monopole detection

Monopole condensation is gauge invariant

Abstract

A direct connection is proved between the Non-Abelian Bianchi Identities and the Abelian Bianchi identities for the 't Hooft tensor in a generic gauge; the existence of a magnetic current is related to the violation of NABI's. Using this relation it is shown that not all gauges are equivalent to detect monopoles on the lattice, that e.g. the Maximal Abelian Gauge is a legitimate choice while the Landau gauge is not. Nevertheless monopole condensation is found to be a gauge invariant property.