Thursday, February 7, 2013

1302.1507 (R. L. Mkrtchyan)

Nonperturbative universal Chern-Simons theory    [PDF]

R. L. Mkrtchyan
Closed simple integral representation through Vogel's universal parameters is found both for perturbative and nonperturbative parts of free energy of Chern-Simons theory on $S^3$. This proves the universality of Chern-Simons partition function. For classical groups partition function 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 K\"ahler parameters, etc.
View original: http://arxiv.org/abs/1302.1507

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