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

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.Comment: 26 pages, AMS-Latex; comparison of metrics done differently and in greater detail; version submitte