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arXiv · hep-th/9708006

SU(N) Monopoles and Platonic Symmetry

Conor Houghton·Paul Sutcliffe
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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.

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Conor Houghton, Paul Sutcliffe. 1997-08-02. SU(N) Monopoles and Platonic Symmetry. https://doi.org/10.1063/1.532152

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