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Communications in Mathematical Physics

, Volume 299, Issue 1, pp 255–282 | Cite as

On the Tetrahedrally Symmetric Monopole

  • H. W. Braden
  • V. Z. Enolski
Article

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.

Keywords

Line Bundle Elliptic Curve Elliptic Curf Elliptic Function Theta Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of MathematicsEdinburgh UniversityEdinburghU.K
  2. 2.Institute of MagnetismNational Academy of Sciences of UkraineKyivUkraine

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