Resurgence matches quantization. (7th March 2017)

• Record Type: Journal Article
• Authors: Couso-Santamaría, Ricardo; Mariño, Marcos; Schiappa, Ricardo
• Is Part Of: Journal of physics. Volume 50:Number 14(2017)
• Publication Date: 2017-03-07
• Subjects: resurgence -- quantization -- string theory -- transseries -- spectral theory -- stokes phenomenon -- topological strings; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa5e01
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: 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 P 2 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.