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

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 ph...

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Main Authors:	Peng eGao, Michael R. Douglas
Format:	Article
Language:	English
Published:	Frontiers Media S.A. 2013-12-01
Series:	Frontiers in Physics
Subjects:	string theory Calabi-Yau manifolds sigma model nonlinear sigma model modular invariance
Online Access:	http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00026/full

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spelling	doaj-ac74e3093aff4cc7aa04559637dbb6762020-11-24T23:20:22ZengFrontiers Media S.A.Frontiers in Physics2296-424X2013-12-01110.3389/fphy.2013.0002666230Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma modelsPeng eGao0Michael R. Douglas1Simons Center for Geometry and Physics, Stony BrookSimons Center for Geometry and Physics, Stony BrookWe 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.http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00026/fullstring theoryCalabi-Yau manifoldssigma modelnonlinear sigma modelmodular invariance
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Peng eGao Michael R. Douglas
spellingShingle	Peng eGao Michael R. Douglas Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models Frontiers in Physics string theory Calabi-Yau manifolds sigma model nonlinear sigma model modular invariance
author_facet	Peng eGao Michael R. Douglas
author_sort	Peng eGao
title	Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
title_short	Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
title_full	Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
title_fullStr	Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
title_full_unstemmed	Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
title_sort	geodesics on calabi-yau manifolds and winding states in nonlinear sigma models
publisher	Frontiers Media S.A.
series	Frontiers in Physics
issn	2296-424X
publishDate	2013-12-01
description	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.
topic	string theory Calabi-Yau manifolds sigma model nonlinear sigma model modular invariance
url	http://journal.frontiersin.org/Journal/10.3389/fphy.2013.00026/full
work_keys_str_mv	AT pengegao geodesicsoncalabiyaumanifoldsandwindingstatesinnonlinearsigmamodels AT michaelrdouglas geodesicsoncalabiyaumanifoldsandwindingstatesinnonlinearsigmamodels
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Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models

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