Monopoles and Harmonic Maps

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.

Version to appear in J. Math. Phys

References in corpus (1)

• Rational Maps, Monopoles and Skyrmions

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• Weyl Equation and (Non)-Commutative SU(n+1) BPS Monopoles
• Non-trivial Soliton Scattering in Planar Integrable Systems
• Hyperbolic monopoles with continuous symmetries
• The Peculiarity of a Negative Coordinate Axis in Dyonic Solutions of Noncommutative N=4 Super Yang-Mills