Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings

Abstract

This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining explicit results for the one-instanton amplitude at both one and two loops. The holographic description of topological strings in terms of matrix models implies that our nonperturbative results also apply to topological strings on toric Calabi-Yau manifolds. This yields very precise predictions for the large-order behavior of the perturbative genus expansion, both in conventional matrix models and in topological string theory. We test these predictions in detail in various examples, including the quartic matrix model, topological strings on the local curve, and Hurwitz theory. In all these cases we provide extensive numerical checks which heavily support our nonperturbative analytical results. Moreover, since all these models have a critical point describing two-dimensional gravity, we also obtain in this way the large-order asymptotics of the relevant solution to the Painleve I equation, including corrections in inverse genus. From a mathematical point of view, our results predict the large-genus asymptotics of simple Hurwitz numbers and of local Gromov-Witten invariants.

50 pages, 24 figures, JHEP3.cls; v2: added references, added discussion on Painleve I, final version for CNTP

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Cited by in corpus (19)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Nonperturbative aspects of ABJM theory
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• A & B model approaches to surface operators and Toda theories
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• A holomorphic and background independent partition function for matrix models and topological strings
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Seiberg-Witten theory and matrix models
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• Non-perturbative effects and wall-crossing from topological strings
• Chern-Simons theory on L(p,q) lens spaces and Gopakumar-Vafa duality
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• Resummations and Non-Perturbative Corrections
• Multi-instantons in large N Matrix Quantum Mechanics
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Matrix models for extremal and integrated correlators of higher rank
• Topics in Open Topological Strings