Periodic Monopoles

Abstract

This thesis discusses periodic one dimensional arrays of BPS monopoles. An approximation based on the spectral curve is shown to provide an increasingly accurate description of the monopole fields in the limit of large monopole size to period ratio. Away from this limit the periodic monopole is studied by means of the Nahm transform, which leads to a dual system of Hitchin equations on a cylinder. A combination of analytical and numerical techniques is used to study the spatial symmetries of the periodic 2-monopole and its moduli space. In particular, the asymptotic moduli space metric is determined from the Nahm data, and symmetric one parameter families of monopole scattering processes are identified through the core of the moduli space. These ideas are readily applicable to higher charge periodic monopoles.