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}
}
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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19 Citations
Background Citations
5
Methods Citations
2

19 Citations

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Klein's curve

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Spectral curves are transcendental

  • H. Braden
  • Mathematics
    Letters in Mathematical Physics
  • 2021
Some arithmetic properties of spectral curves are discussed: the spectral curve, for example, of a charge $$n\ge 2$$ n ≥ 2 Euclidean BPS monopole is not defined over $$\overline{\mathbb {Q}}$$ Q ¯ if…

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