SU(N) Monopoles and Platonic Symmetry

Details SU(N) Monopoles and Platonic Symmetry SU(N) Monopoles and Platonic Symmetry

1997-08-02

arxiv.org/abs/hep-th/9708006v1

J.Math.Phys. 38 (1997) 5576-5589

Physics

High Energy Physics

High Energy Physics - Theory

14pp, RevTex, two figures made of six Postscript files. To appear in the Journal of Mathematical Physics

Scientific paper

10.1063/1.532152

We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N-1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and SU(5) monopoles. In the moduli space approximation, the SU(4) one-parameter family describes a novel dynamics where the monopoles never separate, but rather, a tetrahedron deforms to its dual. We find a two-parameter family of SU(5) tetrahedral monopoles and compute some geodesics in this submanifold numerically. The dynamics is rich, with the monopoles scattering either once or twice through octahedrally symmetric configurations.

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