The moduli space metric for tetrahedrally symmetric 4-monopoles

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. This equivalence implies that the approximation to the time advance (and WKB quantum phase shift) calculated using the point particle derived metric is exact. ∗Address from September 1995, Institute of Mathematics, University of Kent at Canterbury, Canterbury CT2 7NZ. Email [email protected]