## Abstract

The four-dimensional effective action for D5-branes in generic compact Calabi-Yau orientifolds is computed by performing a Kaluza-Klein reduction. The N = 1 Kähler potential, the superpotential, the gauge-kinetic coupling function and the D-terms are derived in terms of the geometric data of the internal space and of the two-cycle wrapped by the D5-brane. In particular, we obtain the D5-brane and flux superpotential by integrating out four-dimensional three-forms which couple via the Chern-Simons action. Also the infinitesimal complex structure deformations of the two-cycle induced by the deformations of the ambient space contribute to the F-terms. The superpotential can be expressed in terms of relative periods depending on both the open and closed moduli. To analyze this dependence we blow up along the two-cycle and obtain a rigid divisor in an auxiliary compact threefold with negative first Chern class. The variation of the mixed Hodge structure on this blown-up geometry is equivalent to the original deformation problem and can be analyzed by Picard-Fuchs equations. We exemplify the blow-up procedure for a non-compact Calabi-Yau threefold given by the canonical bundle over del Pezzo surfaces.

Original language | English |
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Pages (from-to) | 139-184 |

Number of pages | 46 |

Journal | Nuclear Physics B |

Volume | 816 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 21 Jul 2009 |