Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
We conjecture that a non-flat D-real-dimensional compact Calabi-Yau manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4, has locally length minimizing closed geodesics, and that the number of these with length less than L grows asymptotically as L^{D}. We also outline the ph...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2013-12-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00026/full |
| Summary: | We conjecture that a non-flat D-real-dimensional compact Calabi-Yau manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4, has locally length minimizing closed geodesics, and that the number of these with length less than L grows asymptotically as L^{D}. We also outline the physical arguments behind this conjecture, which involve the claim that all states in a nonlinear sigma model can be identified as 'momentum' and 'winding' states in the large volume limit. |
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| ISSN: | 2296-424X |