Ricardo Schiappa, Ricardo Vaz
Resurgent transseries have recently been shown to be a very powerful construction in order to completely describe 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 an '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-cuts 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 Z_2 symmetric two-cuts set-up, addressing the cases of the quartic matrix model in its two-cuts Stokes phase; the "triple" Penner potential which yields four-point correlation functions in the AGT framework; and the Painleve II equation describing minimal superstrings.
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http://arxiv.org/abs/1302.5138
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