Partial compactification of monopoles and metric asymptotics

TL;DR

This paper develops a partial compactification of the monopole moduli space, revealing detailed asymptotic metric behavior as monopoles decompose into clusters, extending previous known cases.

Contribution

It introduces a new partial compactification of the monopole moduli space and provides a comprehensive asymptotic expansion of its hyperKahler metric.

Findings

Constructed a partial compactification of M_k.

Derived the asymptotic expansion of the metric near the boundary.

Generalized previous asymptotic metric results to higher charge decompositions.

Abstract

We construct a partial compactification of the moduli space, M_k, of SU(2) magnetic monopoles on R^3, wherein monopoles of charge k decompose into widely separated 'monopole clusters' of lower charge going off to infinity at comparable rates. The hyperKahler metric on M_k has a complete asymptotic expansion up to the boundary, the leading term of which generalizes the asymptotic metric discovered by Bielawski, Gibbons and Manton in the case that each lower charge is 1.