Abstract
Resurgent transseries have recently been shown to be a very powerful construction for completely describing nonperturbative phenomena in both matrix models and topological or minimal strings. These solutions encode the full nonperturbative content of a given gauge or string theory, where resurgence relates every (generalized) multi-instanton sector to each other via large-order analysis. The Stokes phase is the adequate gauge theory phase where a ’t Hooft large N expansion exists and where resurgent transseries are most simply constructed. This paper addresses the nonperturbative study of Stokes phases associated to multi-cut solutions of generic matrix models, constructing nonperturbative solutions for their free energies and exploring the asymptotic large-order behavior around distinct multi-instanton sectors. Explicit formulae are presented for the \({\mathbb{Z}_2}\) symmetric two-cut set-up, addressing the cases of the quartic matrix model in its two-cut Stokes phase; the “triple” Penner potential which yields four-point correlation functions in the AGT framework; and the Painlevé II equation describing minimal superstrings.
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Schiappa, R., Vaz, R. The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlevé II Equation. Commun. Math. Phys. 330, 655–721 (2014). https://doi.org/10.1007/s00220-014-2028-7
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DOI: https://doi.org/10.1007/s00220-014-2028-7