Platonic hyperbolic monopoles

Understand

We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry.

• The fields are obtained from instanton data in four-dimensional Euclidean space that are invariant under a circle action, and in most cases the monopole charge is equal to the instanton charge.
• A key ingredient is the identification of a new set of constraints on ADHM instanton data that are sufficient to ensure the circle invariance.
• Unlike for Euclidean monopoles, the formulae for the squared Higgs field magnitude in the examples we construct are rational functions of the coordinates.