### 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.

Original language | English (US) |
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Pages (from-to) | 107-127 |

Number of pages | 21 |

Journal | Communications in Mathematical Physics |

Volume | 324 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1 2013 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Keller, C. A., & Ooguri, H. (2013). Modular Constraints on Calabi-Yau Compactifications.

*Communications in Mathematical Physics*,*324*(1), 107-127. https://doi.org/10.1007/s00220-013-1797-8