Title | Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality |

Publication Type | Journal Article |

Year of Publication | 2010 |

Authors | Brini, A, Griguolo, L, Seminara, D, Tanzini, A |

Journal | J. Geom. Phys. 60 (2010) 417-429 |

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-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel matrix integral representations of the SU(N) CS 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, we perform in full detail the construction of a family of would-be dual closed string backgrounds via conifold geometric transition from T^*L(p,q). We can then explicitly prove 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. |

URL | http://hdl.handle.net/1963/2938 |

DOI | 10.1016/j.geomphys.2009.11.006 |

## Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality

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