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.
Description
Chern–Simons theory on L(p,q) lens spaces and Gopakumar–Vafa duality
%0 Journal Article
%1 Brini2010417
%A Brini, Andrea
%A Griguolo, Luca
%A Seminara, Domenico
%A Tanzini, Alessandro
%D 2010
%J Journal of Geometry and Physics
%K chern-simons lens space theory
%N 3
%P 417 - 429
%R http://dx.doi.org/10.1016/j.geomphys.2009.11.006
%T Chern–Simons theory on lens spaces and Gopakumar–Vafa duality
%U http://www.sciencedirect.com/science/article/pii/S0393044009001892
%V 60
%X 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.
@article{Brini2010417,
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. },
added-at = {2016-08-17T12:44:33.000+0200},
author = {Brini, Andrea and Griguolo, Luca and Seminara, Domenico and Tanzini, Alessandro},
biburl = {https://www.bibsonomy.org/bibtex/2debe1e15cc7fb0307bd0d252160b2061/adamgyenge},
description = {Chern–Simons theory on L(p,q) lens spaces and Gopakumar–Vafa duality},
doi = {http://dx.doi.org/10.1016/j.geomphys.2009.11.006},
interhash = {9b7acb688cd2fb5076019b55fa64214b},
intrahash = {debe1e15cc7fb0307bd0d252160b2061},
issn = {0393-0440},
journal = {Journal of Geometry and Physics },
keywords = {chern-simons lens space theory},
number = 3,
pages = {417 - 429},
timestamp = {2016-08-17T12:44:33.000+0200},
title = {Chern–Simons theory on lens spaces and Gopakumar–Vafa duality },
url = {http://www.sciencedirect.com/science/article/pii/S0393044009001892},
volume = 60,
year = 2010
}