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arXiv · 1301.1687

Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models

Peng Gao·Michael R. Douglas
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Abstract

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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Peng Gao, Michael R. Douglas. 2013-01-08. Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models. https://doi.org/10.3389/fphy.2013.00026

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