Topological charges and the genus of surfaces
High Energy Physics - Theory
2009-10-30 v1 dg-ga
Differential Geometry
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.
Keywords
Cite
@article{arxiv.hep-th/9701038,
title = {Topological charges and the genus of surfaces},
author = {Luis J. Boya and Antonio J. Segui-Santonja},
journal= {arXiv preprint arXiv:hep-th/9701038},
year = {2009}
}
Comments
8 pages, Latex. To be published in Journal of Geommetry and Physics