Dynamics of monopole walls

TL;DR

This paper explores the moduli space of doubly-periodic monopole fields, known as monopole walls, analyzing geodesics that relate to monopole dynamics and revealing unique features due to periodicity.

Contribution

It investigates the moduli space of doubly-periodic monopoles, identifying geodesics as fixed points of symmetries and interpreting their physical significance.

Findings

Identification of geodesics as fixed points of symmetries

Interpretation of geodesics in terms of monopole scattering and bound states

Discovery of novel features due to periodicity

Abstract

The moduli space of centred Bogomolny-Prasad-Sommmerfield 2-monopole fields is a 4-dimensional manifold M with a natural metric, and the geodesics on M correspond to slow-motion monopole dynamics. The best-known case is that of monopoles on R^3, where M 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 M for doubly-periodic fields, which may be visualized as monopole walls. We identify some of the geodesics on M 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.