QCD Monopoles on the Lattice and Gauge Invariance

TL;DR

This paper demonstrates that monopoles are inherently gauge-invariant entities in lattice QCD, and the apparent gauge dependence arises from the detection method's efficiency, which varies with the choice of abelian projection.

Contribution

It proves monopoles are gauge-invariant using non-abelian Bianchi identities, clarifying the gauge dependence of their observed locations and numbers.

Findings

Monopoles are gauge-invariant as physical objects.

Detection efficiency depends on the choice of abelian projection.

The gauge dependence is controllable and well-understood.

Abstract

The long standing problem is solved why the number and the location of monopoles observed in Lattice configurations depend on the choice of the gauge used to detect them, in contrast to the obvious requirement that monopoles, as physical objects, must have a gauge-invariant status. It is proved, by use of non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and controllable way.