1301.1687 (Peng Gao et al.)

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

Peng Gao, Michael R. Douglas

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.

View original: http://arxiv.org/abs/1301.1687