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

Frontiers in Physics

Gao, Peng¹  Douglas, Michael R.¹ 

[1] Simons Center for Geometry and Physics, Stony Brook, Stony Brook, New York, United States

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

DOI  :  10.3389/fphy.2013.00026

学科分类：物理（综合）

来源: Frontiers

【 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】

CC BY