Multi-Instantons and Multi-Cuts

Abstract

We discuss various aspects of multi-instanton configurations in generic multi-cut matrix models. Explicit formulae are presented in the two-cut case and, in particular, we obtain general formulae for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulae show that the instanton gas is ultra-dilute, due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their back-reaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painleve I equation.

34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes; v3: added 1 reference, more minor changes, final version for JMP; v4: more typos corrected

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• Remodeling the B-model
• Les Houches lectures on matrix models and topological strings
• Direct Integration of the Topological String
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Integrability of the holomorphic anomaly equations
• Holomorphic Anomaly in Gauge Theories and Matrix Models
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Cited by in corpus (55)

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• A holomorphic and background independent partition function for matrix models and topological strings
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
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• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
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• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Delayed Deconfinement and the Hawking-Page Transition
• Multi-instantons in minimal string theory and in matrix integrals
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• The Resurgence of the Cusp Anomalous Dimension
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• Finite N from Resurgent Large N
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• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
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• Non-perturbative effects and wall-crossing from topological strings
• Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries
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• Complex saddles in the Gross-Witten-Wadia matrix model
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
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• Parametric dependence of irregular conformal block
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
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• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Crystals of gauged solitons, force free plasma and resurgence
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Instantons and Extreme Value Statistics of Random Matrices
• One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
• Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles
• Analytic Baby Skyrmions at Finite Density
• Large N instantons from topological strings
• On the Riemann-Hilbert approach to asymptotics of tronquée solutions of Painlevé I
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Capturing the cascade: a transseries approach to delayed bifurcations
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Phase space and phase transitions in the Penner matrix model with negative coupling constant