2013/02/28 by Ricardo Schiappa, Ricardo Vaz · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/s00220-014-2028-7
67 pages, 12 figures; v2: minor changes, final version in CMP
arxiv created 2015/01/05 · arxiv updated 2015/06/15
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-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 Z2 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 Painleve II equation describing minimal superstrings.