Symmetric hyperbolic monopoles

TL;DR

This paper constructs explicit ADHM data for symmetric hyperbolic monopoles, explores their deformations with preserved symmetries, and provides detailed expressions for spectral curves and rational maps, advancing understanding of hyperbolic monopole solutions.

Contribution

It introduces explicit ADHM data for axial hyperbolic monopoles and their symmetric deformations, along with formulas for spectral curves and rational maps.

Findings

Explicit ADHM data for axial hyperbolic monopoles

Deformation families preserving symmetries

Expressions for spectral curves and rational maps

Abstract

Hyperbolic monopole solutions can be obtained from circle-invariant ADHM data if the curvature of hyperbolic space is suitably tuned. Here we give explicit ADHM data corresponding to axial hyperbolic monopoles in a simple, tractable form, as well as expressions for the axial monopole fields. The data is deformed into new 1-parameter families preserving dihedral and twisted-line symmetries. In many cases explicit expressions are presented for their spectral curves and rational maps of both Donaldson and Jarvis type.