New hyper-Kaehler manifolds by fixing monopoles

TL;DR

This paper constructs new hyper-Kaehler manifolds by analyzing the infinite monopole mass limit of monopole moduli spaces, including a new family of fixed monopole spaces for SU(4) monopoles.

Contribution

It introduces a novel method to generate hyper-Kaehler manifolds via monopole mass limits and constructs a new family of fixed monopole moduli spaces.

Findings

The Dancer family of hyper-Kaehler manifolds is an example of this construction.

A new family of fixed monopole spaces for SU(4) monopoles is constructed.

The manifolds are nonsingular when monopole positions are distinct.

Abstract

The construction of new hyper-Kaehler manifolds by taking the infinite monopole mass limit of certain Bogomol'nyi-Prasad-Sommerfield monopole moduli spaces is considered. The one-parameter family of hyperkaehler manifolds due to Dancer is shown to be an example of such manifolds. A new family of fixed monopole spaces is constructed. They are the moduli spaces of four SU(4) monopoles, in the infinite mass limit of two of the monopoles. These manifolds are shown to be nonsingular when the fixed monopole positions are distinct.