Nonperturbative universal Chern-Simons theory

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 S3. This proves the universality of that partition function. For classical groups it manifestly satisfy N → −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.