Asymptotic metrics for SU(N)-monopoles with maximal symmetry breaking

TL;DR

This paper calculates the asymptotic metrics for moduli spaces of SU(N) monopoles with maximal symmetry breaking, showing they closely approximate the exact metrics when monopoles are well separated, and introduces new differentiability results.

Contribution

It provides explicit asymptotic metrics for SU(N) monopoles and demonstrates their differentiability properties, extending known results even for SU(2).

Findings

Asymptotic metrics are exponentially close to exact metrics for well-separated monopoles.

Estimates can be differentiated term by term in natural coordinates.

Results extend differentiability properties to SU(N) monopoles.

Abstract

We compute the asymptotic metrics for moduli spaces of SU(N) monopoles with maximal symmetry breaking. These metrics are exponentially close to the exact monopole metric as soon as, for each simple root, the individual monopoles corresponding to that root are well separated. We also show that the estimates can be differentiated term by term in natural coordinates, which is a new result even for SU(2) monopoles.