1,483 research outputs found
Cyclic Monopoles, Affine Toda and Spectral Curves
We show that any cyclically symmetric monopole is gauge equivalent to Nahm
data given by Sutcliffe's ansatz, and so obtained from the affine Toda
equations. Further the direction (the Ercolani-Sinha vector) and base point of
the linearising flow in the Jacobian of the spectral curve associated to the
Nahm equations arise as pull-backs of Toda data. A theorem of Accola and Fay
then means that the theta-functions arising in the solution of the monopole
problem reduce to the theta-functions of Toda.Comment: 18 page
On Charge-3 Cyclic Monopoles
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.Comment: 34 pages, 16 figures. Revision: Abstract added and a few small
change
Functional Equations and the Generalised Elliptic Genus
We give a new derivation and characterisation of the generalised elliptic
genus of Krichever-H\"ohn by means of a functional equation.Comment: To be published in the collection honouring Francesco Calogero's
70-th birthda
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