Nonperturbative universal Chern-Simons theory
arXiv:1302.1507 · doi:10.1007/JHEP09(2013)054
Abstract
Closed simple integral representation through Vogel's universal parameters is found both for perturbative and nonperturbative (which is inverse invariant group volume) parts of free energy of Chern-Simons theory on . This proves the universality of that partition function. For classical groups it manifestly satisfy N \rightarrow -N duality, in apparent contradiction with previously used ones. For SU(N) we show that asymptotic of nonperturbative part of our partition function coincides with that of Barnes G-function, recover Chern-Simons/topological string duality in genus expansion and resolve abovementioned contradiction. We discuss few possible directions of development of these results: derivation of representation of free energy through Gopakumar-Vafa invariants, possible appearance of non-perturbative additional terms, 1/N expansion for exceptional groups, duality between string coupling constant and Kähler parameters, etc.
18 pages, Final journal version, references added and refined
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Cited by in corpus (27)
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