Two-Component Reduction of Nahm's Equations and Hyper-elliptic Solution

TL;DR

This paper derives general hyper-elliptic solutions to the two-component reduced Nahm equations, expanding the understanding of monopole solutions and their special elliptic cases.

Contribution

It provides the first comprehensive hyper-elliptic solutions to the two-component reduced Nahm equations, highlighting conditions for elliptic solutions based on monopole charges.

Findings

Hyper-elliptic solutions are explicitly constructed.

Elliptic solutions occur only for specific monopole charge values.

The work extends the solution space of reduced Nahm equations.

Abstract

We find the general hyper-elliptic solutions to the two-component reduced Nahm equations proposed by Hitchin et al. Elliptic solutions are a special case and can appear only for specific values of the monopole charges.