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arXiv · 1006.3408

On Charge-3 Cyclic Monopoles

H. W. Braden·Antonella D'Avanzo·V. Z. Enolski
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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.

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H. W. Braden, Antonella D'Avanzo, V. Z. Enolski. 2010-06-24. On Charge-3 Cyclic Monopoles. https://doi.org/10.1088/0951-7715%2F24%2F3%2F001

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