# On the Tetrahedrally Symmetric Monopole

@article{Braden2009OnTT,
title={On the Tetrahedrally Symmetric Monopole},
author={Harry W. Braden and V. Z. Enolski},
journal={Communications in Mathematical Physics},
year={2009},
volume={299},
pages={255-282}
}
• Published 24 August 2009
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• Communications in Mathematical Physics
We study SU(2) BPS monopoles with spectral curves of the form η3+χ(ζ6+bζ3−1) = 0. Previous work has established a countable family of solutions to Hitchin’s constraint that L2 was trivial on such a curve. Here we establish that the only curves of this family that yield BPS monopoles correspond to tetrahedrally symmetric monopoles. We introduce several new techniques making use of a factorization theorem of Fay and Accola for theta functions, together with properties of the Humbert variety. The…
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We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the
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