A Monopole Metric

TL;DR

This paper explicitly computes the metric on the moduli space of tetrahedrally-symmetric charge four SU(2) monopoles using elliptic integrals and confirms the asymptotic metric matches Gibbons and Manton's up to small corrections.

Contribution

It provides an explicit elliptic integral expression for the monopole moduli space metric and verifies the asymptotic form's accuracy.

Findings

Explicit elliptic integral formula for the metric.

Confirmation of Gibbons and Manton's asymptotic metric accuracy.

Small exponential corrections in the asymptotic regime.

Abstract

We calculate explicitly in terms of complete elliptic integrals the metric on the moduli space of tetrahedrally-symmetric, charge four, SU(2) monopoles. Using this we verify that in the asymptotic regime the metric of Gibbons and Manton is exact up to exponentially suppressed corrections.