Instantons and Monopoles

TL;DR

This paper investigates the relationship between monopoles and instantons in QCD, showing that monopole-antimonopole pairs are associated with the creation of fermion zero modes, linking topological configurations to chiral symmetry breaking.

Contribution

It demonstrates that monopole-antimonopole pairs contribute to instanton-like zero modes, revealing a direct connection between monopoles and instantons in QCD.

Findings

Monopole-antimonopole pairs add one fermion zero mode each.

Monopoles produce long monopole loops in configurations.

Zero modes correspond to instantons of topological charge ±1.

Abstract

This study is part of a research program aimed to investigate the relations between instantons, monopoles, and chiral symmetry breaking. Monopoles are important 3-dimensional topological configurations existing in QCD, which are believed to produce colour confinement. Instantons are 4-dimensional topological configurations and are known to be related to chiral symmetry breaking. To study the relation between monopoles and instantons we generate configurations adding to the vacuum state static monopole-antimonopole pairs of opposite charges by use of a monopole creation operator. We observe that the monopole creation operator only adds long monopole loops to the configurations. We then count the number of fermion zero modes using Overlap fermions as a tool. As a result we find that each monopole-antimonopole pair of magnetic charge one adds one zero mode of chirality $\pm1$, i.e. one instanton of topological charge $\pm1$.