Dynamics of monopole walls

The moduli space of centred Bogomolny–Prasad–Sommerfield 2-monopole fields is a 4-dimensional manifold MM with a natural metric, and the geodesics on MM correspond to slow-motion monopole dynamics. The best-known case is that of monopoles on R3R3, where MM is the Atiyah–Hitchin space. More recently, the case of monopoles periodic in one direction (monopole chains) was studied a few years ago. Our aim in this note is to investigate MM for doubly-periodic fields, which may be visualized as monopole walls. We identify some of the geodesics on MM as fixed-point sets of discrete symmetries, and interpret these in terms of monopole scattering and bound orbits, concentrating on novel features that arise as a consequence of the periodicity.