Resummations and Non-Perturbative Corrections

Abstract

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.

25 pages, 8 figures, v2: published version

References in corpus (6)

• Matrix models from operators and topological strings, 2
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Operators from mirror curves and the quantum dilogarithm
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• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
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Cited by in corpus (5)

• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Exact Instanton Expansion of ABJM Partition Function
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• Exact Chern-Simons / Topological String duality
• Exact solutions to quantum spectral curves by topological string theory