The Moduli Space Metric for Well Separated BPS Monoples

TL;DR

This paper derives the asymptotic metric on the moduli space of well-separated BPS monopoles by modeling their dynamics as geodesic motion, revealing a hyperkähler structure relevant to gauge theory and mathematical physics.

Contribution

It provides an explicit calculation of the asymptotic moduli space metric for multiple BPS monopoles, extending understanding of their geometric and physical properties.

Findings

Derived the asymptotic metric for n monopoles

Confirmed the hyperkähler nature of the moduli space

Provided explicit form of the metric in the asymptotic region

Abstract

The Lagrangian for the motion of $n$ well-separated BPS monopoles is calculated, by treating the monopoles as point particles with magnetic, electric and scalar charges. It can be reinterpreted as the Lagrangian for geodesic motion on the asymptotic region of the $n$-monopole moduli space, thereby determining the asymptotic metric on the moduli space. The metric is hyperk\"ahler, and is an explicit example of a type of metric considered previously.