# Instantons and Monopoles in the Maximally Abelian Gauge

## TL;DR

This paper explores how SU(2) instantons in the Maximally Abelian gauge generate monopole loops, revealing their topological origin and implications for confinement and chiral symmetry breaking.

## Contribution

It demonstrates the relationship between instantons and monopole loops in the Maximally Abelian gauge, including effects of quantum fluctuations and instanton interactions.

## Key findings

- Isolated instantons produce monopole loops within their core.
- Large monopole loops can arise from overlapping instantons.
- In the quantum vacuum, only some monopole loops are topologically related to instantons.

## Abstract

We study the Abelian projection of SU(2) instantons in the Maximally Abelian gauge. We find that in this gauge an isolated instanton produces a closed monopole loop within its core and the size of this loop increases with the core size. We show that this result is robust against the introduction of small quantum fluctuations. We investigate the effects of neighbouring (anti)instantons upon each other and show how overlapping (anti)instantons can generate larger monopole loops. We find, however, that in fields that are typical of the fully quantised vacuum only some of the large monopole loops that are important for confinement have a topological origin. We comment on what this may imply for the role of instantons in confinement and chiral symmetry breaking.