Monopoles and Harmonic Maps

Details Monopoles and Harmonic Maps Monopoles and Harmonic Maps

1999-03-22

arxiv.org/abs/hep-th/9903183v2

J.Math.Phys.40:5440-5455,1999

Physics

High Energy Physics

High Energy Physics - Theory

Version to appear in J. Math. Phys

Scientific paper

10.1063/1.533038

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.

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