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

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

2008-09-09

arxiv.org/abs/0809.1610v2

J.Geom.Phys.60:417-429,2010

Physics

Mathematical Physics

17 pages, 6 figures; references added

Scientific paper

10.1016/j.geomphys.2009.11.006

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.

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