New hyper-Kaehler manifolds by fixing monopoles

Abstract

The construction of new hyper-Ka?hler manifolds by taking the infinite monopole mass limit of certain Bogomol?nyi-Prasad-Sommerfield monopole moduli spaces is considered. The one-parameter family of hyper- Ka?hler 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 SU4 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.