Nonperturbative universal Chern-Simons theory

Understand

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 $S^3$.

• 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.