## Abstract

We study SU(2) BPS monopoles with spectral curves of the form eta (3)+chi(zeta (6)+b zeta (3)-1) = 0. Previous work has established a countable family of solutions to Hitchin's constraint that L (2) 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 geometry leads us to a formulation purely in terms of elliptic functions. A more general conjecture than needed for the stated result is given.

Original language | English |
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Pages (from-to) | 255-282 |

Number of pages | 28 |

Journal | Communications in Mathematical Physics |

Volume | 299 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 2010 |

## Keywords

- CURVES