The moduli space metric for tetrahedrally symmetric 4-monopoles

TL;DR

This paper computes the metric on the moduli space of tetrahedrally symmetric 4-monopoles using numerical methods, revealing agreements with point particle models and novel dynamical insights.

Contribution

It provides the first detailed numerical calculation of the moduli space metric for tetrahedral 4-monopoles, highlighting new dynamical phenomena and metric equivalences.

Findings

Excellent agreement with point particle metric in asymptotic region

Monopoles experience acceleration through cubic configurations

Evidence for a distance equivalence between monopole and point particle moduli spaces

Abstract

The metric on the moduli space of SU(2) charge four BPS monopoles with tetrahedral symmetry is calculated using numerical methods. In the asymptotic region, in which the four monopoles are located on the vertices of a large tetrahedron, the metric is in excellent agreement with the point particle metric. We find that the four monopoles are accelerated through the cubic monopole configuration and compute the time advance. Numerical evidence is presented for a remarkable equivalence between a proper distance in the 4-monopole moduli space and a related proper distance in the point particle moduli space.