Interactions of massless monopole clouds

Abstract

Some spontaneously broken gauge theories with unbroken non-Abelian gauge groups contain massless magnetic monopoles that are realized classically as clouds of non-Abelian field surrounding one or more massive monopoles. We use moduli space methods to investigate the properties of these massless monopole clouds. We show that the natural metric on the Nahm data for a class of $\mathrm{SU}(2M+2)$ solutions with $2M$ massive and $M(2M\ensuremath{-}1)$ massless monopoles can be obtained from that for a simpler class of $\mathrm{SU}(M+1)$ solutions. For the $M=1$ case, we show that the Nahm data metric is isomorphic to the metric for the moduli of the BPS solutions, thus verifying a previously conjectured result. For $M=2$ we use our results and the moduli space approximation to obtain an effective Lagrangian for an axially symmetric class of solutions. Using this Lagrangian, we study the interactions between the two types of clouds that appear. We show that, although the static spacetime field configurations suggest that the clouds might be rather diffuse, in scattering processes they behave as if they were relatively thin hard shells.