HyperKähler Quotient Construction of BPS Monopole Moduli Spaces

Abstract:

We use the HyperKähler quotient of flat space to obtain some monopole moduli space metrics in explicit form. Using this new description, we discuss their topology, completeness and isometries. We construct the moduli space metrics in the limit when some monopoles become massless, which corresponds to non-maximal symmetry breaking of the gauge group. We also introduce a new family of HyperKähler metrics which, depending on the “mass parameter” being positive or negative, tend to either the asymptotic metric on the moduli space of many SU(2) monopoles, or to previously unknown metrics. These new metrics are singular or complete depending on the particular choice of the level set of the moment map. The singular metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups. Finally, we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow.