## Abstract

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi-Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin functional is studied at one loop. It is found that the genus one free energy of the topological B-model disagrees with the one-loop free energy of the minimal Hitchin functional. However, the topological B-model does agree at one-loop order with the extended Hitchin functional, which also defines by critical points a generalized Calabi-Yau structure. The dependence of the one-loop result on a background metric is studied, and a gravitational anomaly is found for both the B-model and the extended Hitchin model. The anomaly reduces to a volume-dependent factor if one computes for only Ricci-flat Kähler metrics.

Original language | English (US) |
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Pages (from-to) | 21-51 |

Number of pages | 31 |

Journal | Letters in Mathematical Physics |

Volume | 74 |

Issue number | 1 |

DOIs | |

State | Published - Oct 2005 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Generalized complex structures
- Topological B-model
- Topological M-theory