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Topological charges and the genus of surfaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Aug 1997Embargo end date: 01 Jan 1997Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 23, pages 76-82 (issn: 0393-0440,

Authors: Antonio J. Segui-Santonja; Luis J. Boya;

doi: 10.1016/s0393-0440(96)00048-4 , 10.48550/arxiv.hep-th/9701038

arXiv: http://arxiv.org/abs/hep-th/9701038

Topological charges and the genus of surfaces

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Abstract

We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is even. The moduli space of complex dimension B(g)=3(g-1) corresponds precisely to the freedom to choosing the configuration with n solitons of arbitrary positions and velocities. We speculate also that the odd soliton states will describe the unoriented surfaces.

8 pages, Latex. To be published in Journal of Geommetry and Physics

Related Organizations

University of Zaragoza
Spain

Keywords

sine-Gordon equation, High Energy Physics - Theory, Mathematics - Differential Geometry, FOS: Physical sciences, topological charges, Riemann surfaces, KdV equations (Korteweg-de Vries equations), High Energy Physics - Theory (hep-th), Differential Geometry (math.DG), solitons, FOS: Mathematics, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), moduli spaces

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