### Abstract

We establish a new weak coupling limit in F-theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter t such that computations in the local model become exact as t → 0. More generally, we advocate a modular approach where compact Calabi-Yau geometries are obtained by gluing together local pieces (log Calabi-Yau spaces) into a normal crossing variety and smoothing, in analogy with a similar cutting and gluing approach to topological field theories. We further argue for a holographic relation between F-theory on a degenerate Calabi-Yau and a dual theory on its boundary, which fits nicely with the gluing construction.

Original language | English (US) |
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Pages (from-to) | 665-738 |

Number of pages | 74 |

Journal | Pure and Applied Mathematics Quarterly |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2013 |

### Keywords

- Calabi-Yau
- Elliptic fibration
- F-theory
- Semi-stable degeneration
- Smoothing
- String compactification
- Variation of hodge structure

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Pure and Applied Mathematics Quarterly*,

*9*(4), 665-738. https://doi.org/10.4310/PAMQ.2013.v9.n4.a4