Journal Article Resummations and non-perturbative corrections

Hatsuda, Yasuyuki  ,  Okuyama, Kazumi

(9)  , p.051 , 2015-09-09 , SPRINGER
We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and obtain a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling g s , we find that it includes not only the M-theoretic resummation à la Gopakumar and Vafa, but also a non-perturbative correction in g s . Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:​1306.​1734. Various other examples are also presented.

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