Monopoles from Rational Maps

TL;DR

This paper introduces a numerical algorithm to compute SU(2) BPS monopole fields and energy densities from rational maps, facilitating the study of monopole configurations with symmetry.

Contribution

It presents a new numerical method to derive monopole fields from rational maps, bridging a gap between theoretical moduli space descriptions and practical computations.

Findings

Successfully computed monopole fields for symmetric examples

Demonstrated the algorithm's effectiveness in practical scenarios

Provided visualizations of energy density distributions

Abstract

The moduli space of charge k SU(2) BPS monopoles is diffeomorphic to the moduli space of degree k rational maps between Riemann spheres. In this note we describe a numerical algorithm to compute the monopole fields and energy density from the rational map. The results for some symmetric examples are presented.