Polyhedral Scattering of Fundamental Monopoles

TL;DR

This paper models the scattering of multiple fundamental monopoles using geodesic paths on a hyperkähler manifold, revealing complex bouncing polyhedral configurations during monopole interactions.

Contribution

It introduces a variational method to construct scaling geodesics on the Lee-Weinberg-Yi manifold, describing monopole scattering as bouncing polyhedra.

Findings

Monopole scattering can be represented by contracting and expanding polyhedra.

Different monopole masses lead to nested bouncing polyhedra.

Results are relevant to the dynamics of well-separated SU(2) 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 hyperkahler Lee-Weinberg-Yi manifold. In this paper 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.