# Instantons in the Maximally Abelian Gauge

## TL;DR

This paper studies how instantons in SU(2) gauge theory behave under the Maximally Abelian gauge, revealing monopole loops and their relation to gauge fixing and instanton interactions.

## Contribution

It identifies solutions with monopole loops in the MA gauge and analyzes how the gauge fixing functional behaves, highlighting the influence of instanton interactions.

## Key findings

- Monopole loops of radius R centered on instantons are solutions in the MA gauge.
- The gauge fixing functional decreases as monopole loop size shrinks, with the minimum at the singular gauge.
- Interactions with anti-instantons can excite monopole loops, affecting gauge configurations.

## Abstract

We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$ instanton in continuum gauge theory. We find that there is a class of solutions to the differential MA gauge condition with circular monopole loops of radius $R$ centered on the instanton of width $\rho$. However, the MA gauge fixing functional $G$ decreases monotonically as $R/\rho \rightarrow 0$. Its global minimum is the instanton in the singular gauge. We point out that interactions with nearby anti-instantons are likely to excite these monopole loops.