Modular Constraints on Calabi-Yau Compactifications

Creators: Keller, Christoph A.; Ooguri, Hirosi

Abstract

We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.

Additional Information

© Springer-Verlag Berlin Heidelberg. Received: 18 October 2012; Accepted: 28 January 2013. We thank T. Eguchi, M. Freedman, M. Gaberdiel, S. Hellerman, C. Schmidt-Colinet, W. Taylor, C. Vafa and S.-T. Yau for useful discussions. We thank D. Friedan and T. Hübsch for their comments on the earlier version of the paper. We thank the hospitality of the Aspen Center for Physics (NSF grant 1066293) and the Simons Center for Geometry and Physics. This work is supported in part by U.S. DOE grant DE-FG03-92-ER40701. The work of CAK is also supported in part by the John A. McCone Postdoctoral Fellowship at Caltech and U.S. DOE grant DE-FG02-96ER40959. The work of HO is also supported in part by a Simons Investigator award from the Simons Foundation, the Fred Kavli Professorship at Caltech, and by the WPI Initiative of MEXT of Japan and JSPS Grant-in-Aid for Scientific Research C-23540285.

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