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arxiv 1505.07460 v2 pith:VBDBW4LF submitted 2015-05-27 hep-th math-phmath.MP

Resummations and Non-Perturbative Corrections

Yasuyuki Hatsuda , Kazumi Okuyama This is my paper
classification hep-th math-phmath.MP
keywords non-perturbativeresummationborelcorrectioncorrectionsfindintegrallarge
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 find a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling gs, we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in gs. 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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