## Abstract

We consider aspects of Chern-Simons theory on L (p, q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-S U (2) cyclic quotients of the conifold. To this aim we find, on one hand, a useful matrix integral representation of the S U (N) C S partition function in a generic flat background for the whole L (p, q) family and provide a solution for its large N dynamics; on the other hand, we perform in full detail the construction of a family of would-be dual closed string backgrounds through conifold geometric transition from T^{*} L (p, q). We can then explicitly prove the claim in [5] that Gopakumar-Vafa duality in a fixed vacuum fails in the case q > 1, and briefly discuss how it could be restored in a non-perturbative setting.

Original language | English |
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Pages (from-to) | 417-429 |

Number of pages | 13 |

Journal | Journal of Geometry and Physics |

Volume | 60 |

Issue number | 3 |

Early online date | 10 Nov 2009 |

DOIs | |

Publication status | Published - 1 Mar 2010 |

## Keywords

- Chern-Simons theory
- Geometric transitions
- Gopakumar-Vafa
- Large N duality
- Open-closed duality
- Random matrices
- Topological strings

## ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology