Scattering of massless and massive monopoles in an SU(N) theory

Abstract

We use the moduli space approximation to study the time evolution of magnetically charged configurations in a theory with an SU(N+2) gauge symmetry spontaneously broken to U(1) x SU(N) x U(1). We focus on configurations containing two massive and N-1 massless monopoles. The latter do not appear as distinct objects, but instead coalesce into a cloud of non-Abelian field. We find that at large times the cloud and the massless particles are decoupled, with separately conserved energies. The interaction between them occurs through a scattering process in which the cloud, acting very much like a thin shell, contracts and eventually bounces off the cores of the massive monopoles. The strength of the interaction, as measured, e.g., by the amount of energy transfer, tends to be greatest if the shell is small at the time that it overlaps the massive cores. We also discuss the corresponding behavior for the case of the SU(3) multimonopole solutions studied by Dancer.