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Resurgence matches quantization

The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been possible to give a nonperturbative definition of the topological-s...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2017-04, Vol.50 (14), p.145402
Main Authors: Couso-Santamaría, Ricardo, Mariño, Marcos, Schiappa, Ricardo
Format: Article
Language:English
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Summary:The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been possible to give a nonperturbative definition of the topological-string partition function. On the other hand, using techniques of resurgence and transseries, it has been possible to extend the string (asymptotic) perturbative expansion into a transseries involving nonperturbative instanton sectors. Within the specific example of the local P2 toric Calabi-Yau threefold, the present work shows how the Borel-Padé-Écalle resummation of this resurgent transseries, alongside occurrence of Stokes phenomenon, matches the string-theoretic partition function obtained via quantization of the mirror curve. This match is highly non-trivial, given the unrelated nature of both nonperturbative frameworks, signaling at the existence of a consistent underlying structure.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aa5e01