The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation

Abstract

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 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 Painleve II equation describing minimal superstrings.

67 pages, 12 figures; v2: minor changes, final version in CMP

References in corpus (15)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Open string amplitudes and large order behavior in topological string theory
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Les Houches lectures on matrix models and topological strings
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Holomorphic anomaly and matrix models
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Universality and asymptotics of graph counting problems in nonorientable surfaces
• Complex Path Integrals and the Space of Theories
• Analytic Study for the String Theory Landscapes via Matrix Models

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• Complex Path Integrals and the Space of Theories
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
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• Resurgent transseries $\&$ Dyson-Schwinger equations
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
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• Quantization of classical spectral curves via topological recursion
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• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
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• Phase space and phase transitions in the Penner matrix model with negative coupling constant
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• Supersymmetric Quantum Mechanics and Path Integrals
• On the Perturbed Second Painlevé Equation