Monopoles on R^5 and Generalized Nahm's equations

TL;DR

This paper develops a twistorial approach to define monopoles on R^5, introducing a new spectral curve method and a system of equations analogous to Nahm's equations, extending monopole theory to higher dimensions.

Contribution

It introduces a twistorial framework for R^5 monopoles, develops a Hitchin-Ward transform, and derives a new system of equations similar to Nahm's equations for higher-dimensional monopoles.

Findings

Established a twistor theory for R^5.

Developed a Hitchin-Ward transform for monopoles.

Derived a new system of equations analogous to Nahm's equations.

Abstract

Our approach to define monopoles is twistorial and we start by developing the twistor theory of R^5, which is an analogue of the twistor theory for R^3 developed by Hitchin. Using this, we describe a Hitchin-Ward transform for R^5, that gives monopoles. In order for us to construct monopoles we make use of spectral curves. Then, using those spectral curves we find a new system of equations, analogue to the Nahm's equations.