Geodesics on Calabi-Yau manifolds and winding states in non-linear sigma models - Gao, Peng; Douglas, Michael R. (Frontiers in Physics, 2013)
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.