Monopoles from Instantons

TL;DR

This paper explores the connection between instantons and monopoles in Abelian gauges, revealing how instanton defects relate to monopole loops and their topological properties using a novel auxiliary bundle method.

Contribution

It introduces a new method using an auxiliary Abelian fiber bundle to analyze the relationship between instantons, monopoles, and topological invariants.

Findings

Instanton defects are pointlike and evolve into monopole loops with twist.

The interplay between magnetic charge, twist, and instanton number is characterized by a Hopf invariant.

A new auxiliary bundle method facilitates the analysis of topological relations.

Abstract

The relation between defects of Abelian gauges and instantons is discussed for explicit examples in the Laplacian Abelian gauge. The defect coming from an instanton is pointlike and becomes a monopole loop with twist upon perturbation. The interplay between magnetic charge, twist and instanton number - encoded as a Hopf invariant - is investigated with the help of a new method, an auxiliary Abelian fibre bundle.