Massless monopoles and the moduli space approximation

TL;DR

This paper examines the limits of the moduli space approximation in theories with massless monopoles, showing it works well until high cloud velocities, after which wavefront effects dominate.

Contribution

It demonstrates the applicability and limitations of the moduli space approximation in non-Abelian gauge theories with massless monopoles through numerical comparison.

Findings

The approximation diverges at high cloud velocities.

A spherical wavefront forms and propagates at light speed.

The approximation remains valid behind the wavefront.

Abstract

We investigate the applicability of the moduli space approximation in theories with unbroken non-Abelian gauge symmetries. Such theories have massless magnetic monopoles that are manifested at the classical level as clouds of non-Abelian field surrounding one or more massive monopoles. Using an SO(5) example with one massive and one massless monopole, we compare the predictions of the moduli space approximation with the results of a numerical solution of the full field equations. We find that the two diverge when the cloud velocity becomes of order unity. After this time the cloud profile approximates a spherical wavefront moving at the speed of light. In the region well behind this wavefront the moduli space approximation continues to give a good approximation to the fields. We therefore expect it to provide a good description of the motion of the massive monopoles and of the transfer of energy between the massive and massless monopoles.