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On Charge-3 Cyclic Monopoles

Mathematical Physics 2015-05-19 v2 High Energy Physics - Theory Differential Geometry math.MP

Abstract

We determine the spectral curve of charge 3 BPS su(2) monopoles with C_3 cyclic symmetry. The symmetry means that the genus 4 spectral curve covers a (Toda) spectral curve of genus 2. A well adapted homology basis is presented enabling the theta functions and monopole data of the genus 4 curve to be given in terms of genus 2 data. The Richelot correspondence, a generalization of the arithmetic mean, is used to solve for this genus 2 curve. Results of other approaches are compared.

Cite

@article{arxiv.1006.3408,
  title  = {On Charge-3 Cyclic Monopoles},
  author = {H. W. Braden and Antonella D'Avanzo and V. Z. Enolski},
  journal= {arXiv preprint arXiv:1006.3408},
  year   = {2015}
}

Comments

34 pages, 16 figures. Revision: Abstract added and a few small changes

R2 v1 2026-06-21T15:37:34.364Z