# Crystal Volumes and Monopole Dynamics

## TL;DR

This paper explores the dynamics of doubly periodic monopoles by relating their moduli space's Kähler potential to geometric volumes in Euclidean space, providing insights into their structure and behavior.

## Contribution

It establishes a novel connection between the Kähler potential of monopole moduli space and Euclidean volume calculations, advancing understanding of monopole wall dynamics.

## Key findings

- Derived a relation between Kähler potential and Euclidean volume.
- Characterized the moduli space as hyperkähler and non-compact.
- Linked monopole dynamics to geometric volume regions.

## Abstract

The low velocity dynamic of a doubly periodic monopole, also called a monopole wall or monowall for short, is described by geodesic motion on its moduli space. This moduli space is hyperkaehler and non-compact. We establish a relation between the Kaehler potential of this moduli space and the volume of a region in Euclidean three-space cut out by a plane arrangement associated with each monowall.