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 language | English |
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Title of host publication | XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS |
Editors | P Kielanowski, V Buchstaber, A Odzijewicz, M Schlichenmaier, T Voronov |
Place of Publication | MELVILLE |
Publisher | American Institute of Physics |
Pages | 53-67 |
Number of pages | 15 |
ISBN (Print) | 978-0-7354-0861-6 |
Publication status | Published - 2010 |
Event | 29th Workshop on Geometric Methods in Physics - Bialowieza Duration: 27 Jun 2010 → 3 Jul 2010 |
Conference
Conference | 29th Workshop on Geometric Methods in Physics |
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City | Bialowieza |
Period | 27/06/10 → 3/07/10 |