Monopoles and Harmonic Maps

TL;DR

This paper explores the relationship between SU(N) monopoles and harmonic maps, providing explicit examples and extending the construction to hyperbolic space, thereby advancing understanding of monopole solutions.

Contribution

It details the construction of monopoles from harmonic maps, including explicit examples and extensions to hyperbolic space, enhancing the theoretical framework.

Findings

Explicit examples of spherically symmetric SU(N) monopoles

Method to obtain monopoles from harmonic maps into complex projective spaces

Extension of the approach to hyperbolic monopoles

Abstract

Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide explicit examples for spherically symmetric SU(N) monopoles with various symmetry breakings. In particular we show how to obtain these monopoles from harmonic maps into complex projective spaces. The approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spherically symmetric SU(N) hyperbolic monopoles.