SU(N) Monopoles and Platonic Symmetry

Abstract

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.

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

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• Duality and confinement in SO(N) gauge theories
• Cyclic Monopoles, Affine Toda and Spectral Curves
• Nahm Data and the Mass of 1/4-BPS States
• Construction of Nahm data and BPS monopoles with continuous symmetries
• Weyl Equation and (Non)-Commutative SU(n+1) BPS Monopoles