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

Frontiers in Physics

Michael R. Douglas¹  Peng eGao¹ 

[1] Simons Center for Geometry and Physics, Stony Brook;

关键词: string theory;    Calabi-Yau manifolds;    sigma model;    nonlinear sigma model;    modular invariance;   

DOI  :  10.3389/fphy.2013.00026

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown