A note on monopole moduli spaces

TL;DR

This paper explores the structure and stratification of monopole moduli spaces for arbitrary symmetry breaking and compact Lie groups, proposing conjectures about their geometric properties and calculating dimensions of their components.

Contribution

It extends the stratification definition of monopole moduli spaces to arbitrary compact Lie groups and conjectures hyperKahler metrics on their strata.

Findings

Dimensions of strata and submanifolds are multiples of four.

Each stratum is a union of submanifolds with conjectured hyperKahler metrics.

The structure applies to arbitrary symmetry breaking and compact Lie groups.

Abstract

We discuss the structure of the framed moduli space of Bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact Lie groups. We show that each stratum is a union of submanifolds for which we conjecture that the natural $L^2$ metric is hyperKahler. The dimensions of the strata and of these submanifolds are calculated, and it is found that for the latter, the dimension is always a multiple of four.