Detecting monopoles on the lattice

TL;DR

This paper investigates why magnetic monopoles detected on lattice configurations appear gauge dependent, revealing that monopoles are gauge invariant but detection efficiency varies with gauge choice, using Non-Abelian Bianchi Identities.

Contribution

It demonstrates that monopoles are gauge invariant and explains how detection methods' efficiency depends on gauge choice, bridging different gauge conditions.

Findings

Monopoles are gauge invariant according to Non-Abelian Bianchi Identities.

Detection efficiency varies between gauges, from all monopoles observed to none.

A class of gauges interpolates between maximal Abelian and Landau gauges.

Abstract

We address the issue why the number and the location of magnetic monopoles detected on lattice configurations are gauge dependent, in contrast with the physical expectation that monopoles have a gauge invariant status. By use of the Non-Abelian Bianchi Identities we show that monopoles are gauge invariant, but the efficiency of the technique usually adopted to detect them depends on the choice of the gauge in a well understood way. In particular we have studied a class of gauges which interpolates between the Maximal Abelian gauge, where all monopoles are observed, and the Landau gauge, where all monopoles escape detection.