Monopole Scattering with a Twist

TL;DR

This paper introduces a novel class of monopole scattering processes derived from symmetric geodesics in the moduli space, revealing complex dynamics including symmetry restoration and new Higgs field zero phenomena.

Contribution

It constructs specific symmetric geodesics in monopole moduli space and demonstrates their role in describing new monopole scattering behaviors with rich symmetry dynamics.

Findings

Monopoles can form regular solids during scattering.

Discovered monopoles with more Higgs zeros than monopole charge.

Numerical simulations reveal complex Higgs zero dynamics.

Abstract

By imposing certain combined inversion and rotation symmetries on the rational maps for SU(2) BPS monopoles we construct geodesics in the monopole moduli space. In the moduli space approximation these geodesics describe a novel kind of monopole scattering. During these scattering processes axial symmetry is instantaneously attained and, in some, monopoles with the symmetries of the regular solids are formed. The simplest example corresponds to a charge three monopole invariant under a combined inversion and 90 degree rotation symmetry. In this example three well-separated collinear unit charge monopoles coalesce to form first a tetrahedron, then a torus, then the dual tetrahedron and finally separate again along the same axis of motion. We explicitly construct the spectral curves in this case and use a numerical ADHMN construction to compute the energy density at various times during the motion. We find that the dynamics of the zeros of the Higgs field is extremely rich and we discover a new phenomenon; there exist charge k SU(2) BPS monopoles with more than k zeros of the Higgs field.