Monopoles and clusters

TL;DR

This paper introduces hyperkähler manifolds that model the asymptotic behavior of SU(2)-monopole metrics, showing exponential approximation similar to the Gibbons-Manton metric, and provides insights into monopole breakdown into lower charges.

Contribution

It defines new hyperkähler manifolds that accurately describe monopole asymptotics and quantifies the exponential rate of approximation to the monopole metric.

Findings

Hyperkähler manifolds model monopole asymptotics.

Exponential rate of metric approximation.

Insights into monopole breakdown into lower charges.

Abstract

We define and study certain hyperkaehler manifolds which capture the asymptotic behaviour of the SU(2)-monopole metric in regions where monopoles break down into monopoles of lower charges. The rate at which these new metrics approximate the monopole metric is exponential, as for the Gibbons-Manton metric.