On the Existence of Non-Abelian Monopoles: the Algebro-Geometric Approach

H. W. Braden, V. Z. Enolski

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We develop the Atiyah-Drinfeld-Manin-Hitchin-Nahm construction to study SU(2) non-abelian charge 3 monopoles within the algebro-geometric method. The method starts with finding an algebraic curve, the monopole spectral curve, subject to Hitchin's constraints. We take as the monopole curve the genus four curve that admits a C-3 symmetry, eta(3)+alpha eta zeta(2)+beta zeta(6)+gamma zeta(3)-beta = 0, with real parameters alpha, beta and gamma. In the case alpha = 0 we prove that the only suitable values of gamma/beta are +/- 5 root 2 (beta is given below) which corresponds to the tetrahedrally symmetric solution. We then extend this result by continuity to non-zero values of the parameter alpha and find finally a new one-parameter family of monopole curves with C-3 symmetry.

Original languageEnglish
Title of host publicationXXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS
EditorsP Kielanowski, V Buchstaber, A Odzijewicz, M Schlichenmaier, T Voronov
Place of PublicationMELVILLE
PublisherAmerican Institute of Physics
Pages53-67
Number of pages15
ISBN (Print)978-0-7354-0861-6
Publication statusPublished - 2010
Event29th Workshop on Geometric Methods in Physics - Bialowieza
Duration: 27 Jun 20103 Jul 2010

Conference

Conference29th Workshop on Geometric Methods in Physics
CityBialowieza
Period27/06/103/07/10

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