On the Tetrahedrally Symmetric Monopole |
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Authors: | H. W. Braden V. Z. Enolski |
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Affiliation: | 1. School of Mathematics, Edinburgh University, Edinburgh, U.K 2. Institute of Magnetism, National Academy of Sciences of Ukraine, Kyiv, Ukraine
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Abstract: | We study SU(2) BPS monopoles with spectral curves of the form η 3+χ(ζ 6+b ζ 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. |
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