Gauge Invariant Monopoles in SU(2) Gluodynamics

TL;DR

This paper proposes a gauge invariant topological method to define monopole charge in SU(2) gluodynamics, using Wilson loops to ensure gauge invariance and accurately count monopoles in various gauge field configurations.

Contribution

It introduces a novel gauge invariant monopole charge definition based on hedgehog configurations and Wilson loops, applicable to pure and broken gauge symmetries.

Findings

Defines monopole charge via Wilson loops

Ensures gauge invariance of monopole counting

Works for both broken and unbroken gauge symmetries

Abstract

We introduce a gauge invariant topological definition of monopole charge in pure SU(2) gluodynamics. The non-trivial topology is provided by hedgehog configurations of the non-Abelian field strength tensor on the two-sphere surrounding the monopole. It is shown that this definition can be formulated entirely in terms of Wilson loops which makes the gauge invariance manifest. Moreover, it counts correctly the monopole charge in case of spontaneously broken gauge symmetry and of pure Abelian gauge fields.