Modular Constraints on Calabi-Yau Compactifications

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.

24 pages, 5 figures; v3: corrected typos and an error in the asymptotic bound. Version to appear in CMP

References in corpus (4)

• Notes on the K3 Surface and the Mathieu group M_24
• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• Mathieu Moonshine in the elliptic genus of K3
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity

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