Monopole fission

Abstract

There is a 4N-dimensional moduli space of SU(2) BPS monopoles with charge N, but introducing a Higgs potential removes this degeneracy and yields a repulsive force between monopoles. However, if a point in the BPS monopole moduli space is sufficiently symmetric, then it flows to a similar non-BPS saddle point solution once the Higgs potential is introduced. Monopole fission, into constituent monopoles with lower charges, results from symmetry breaking perturbations of such saddle point solutions. This fission is investigated numerically, by evolving the gradient flow equations of the Yang-Mills-Higgs theory, with initial conditions and symmetry breaking perturbations created using rational maps between Riemann spheres. The results resemble components of BPS monopole scattering processes obtained within the geodesic approximation for low speed monopole dynamics.