Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
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.
Keywords
Cite
@article{arxiv.0809.1610,
title = {Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality},
author = {Andrea Brini and Luca Griguolo and Domenico Seminara and Alessandro Tanzini},
journal= {arXiv preprint arXiv:0809.1610},
year = {2011}
}
Comments
17 pages, 6 figures; references added