AUTHOR=Gao Peng , Douglas Michael R.

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

JOURNAL=Frontiers in Physics

VOLUME=1

YEAR=2013

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2013.00026

DOI=10.3389/fphy.2013.00026

ISSN=2296-424X

ABSTRACT=<p>We conjecture that a non-flat <italic>D</italic>-real-dimensional compact Calabi-Yau manifold, such as a quintic hypersurface with <italic>D</italic> = 6, or a K3 manifold with <italic>D</italic> = 4, has locally length minimizing closed geodesics, and that the number of these with length less than <italic>L</italic> grows asymptotically as <italic>L</italic><sup><italic>D</italic></sup>. We also outline the physical arguments behind this conjecture, which involve the claim that all states in a non-linear sigma model can be identified as “momentum” and “winding” states in the large volume limit.</p>