Construction of Exact Solutions to Nahm's Equations for the Multimonopole

TL;DR

This paper constructs explicit high-rank solutions to Nahm's equations for multimonopoles, utilizing spectral curves and polynomial bases to integrate the eigenline bundle flow.

Contribution

It provides a novel explicit construction of solutions to Nahm's equations for multimonopoles with known spectral curves.

Findings

Explicit solutions for high-rank Nahm's equations

Construction of polynomial bases for eigenline bundle flow

Application to Dirac multimonopoles

Abstract

We construct high rank solutions to Nahm's equations for boundary conditions that correspond to the Dirac multimonopole. Here, the spectral curve is explicitly known and we achieve the integration by constructing a basis of polynomial tuples that forms a frame for the flow of the eigenline bundle over the curve.