Polyhedral scattering of fundamental monopoles

Abstract

The dynamics of n slowly moving fundamental monopoles in the SU(n+1) BPS Yang–Mills–Higgs theory can be approximated by geodesic motion on the 4n-dimensional hyperkähler Lee–Weinberg–Yi manifold. In this article we apply a variational method to construct some scaling geodesics on this manifold. These geodesics describe the scattering of n monopoles which lie on the vertices of a bouncing polyhedron; the polyhedron contracts from infinity to a point, representing the spherically symmetric n-monopole, and then expands back out to infinity. For different monopole masses the solutions generalize to form bouncing nested polyhedra. The relevance of these results to the dynamics of well separated SU(2) monopoles is also discussed.