Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

Abstract

We develop techniques to compute multi-instanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding trans-series solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multi-instanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its double-scaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that trans-series solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multi-instanton sectors of the matrix model

50 pages, 12 figures, comments and references added, small corrections

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Cited by in corpus (97)

• 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
• Nonperturbative aspects of ABJM theory
• A Primer on Resurgent Transseries and Their Asymptotics
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
• Generating Non-perturbative Physics from Perturbation Theory
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Membrane instantons from a semiclassical TBA
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Structure of Lefschetz thimbles in simple fermionic systems
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Resurgence in Extended Hydrodynamics
• Hydrodynamics, resurgence and trans-asymptotics
• A note on perturbation series in supersymmetric gauge theories
• 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
• TBA equations and resurgent Quantum Mechanics
• Multi-Instantons and Multi-Cuts
• Physical Resurgent Extrapolation
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Resumming the string perturbation series
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• A simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix
• Quantum Curves and D-Modules
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Delayed Deconfinement and the Hawking-Page Transition
• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
• Complex Saddles in Two-dimensional Gauge Theory
• Exact Resurgent Trans-series and Multi-Bion Contributions to All Orders
• On 3d extensions of AGT relation
• Holomorphic Anomaly and Quantum Mechanics
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Uniformization and Constructive Analytic Continuation of Taylor Series
• Resurgence Matches Quantization
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Remark on the Dunne-Unsal relation in exact semi-classics
• Finite N from Resurgent Large N
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Non-Perturbative Topological Strings And Conformal Blocks
• Large N duality beyond the genus expansion
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Resurgence of the large-charge expansion
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence in the O(4) sigma model
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Exact multi-instantons in topological string theory
• Localization at large N in Chern-Simons-matter theories
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Wilson loops in unitary matrix models at finite $N$
• Summing over all Topologies in CDT String Field Theory
• Resurgence for superconductors
• From perturbative to non-perturbative in the O(4) sigma model
• Non-perturbative effects and wall-crossing from topological strings
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries
• Complex saddles in the Gross-Witten-Wadia matrix model
• Gradient flows without blow-up for Lefschetz thimbles
• S-duality resurgence in SL(2) Chern-Simons theory
• The Heisenberg XX spin chain and low-energy QCD
• Eigenvalue instantons in the spectral form factor of random matrix model
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Large $N$ expansion of an integrated correlator in $\mathcal{N}=4$ SYM
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Resurgence in the Bi-Yang-Baxter Model
• Resurgence, Painleve Equations and Conformal Blocks
• 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
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Non-Perturbative Random Matrix Model of $\mathcal{N}=2$ JT Supergravity
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• Instantons and Extreme Value Statistics of Random Matrices
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• Exploring High Multiplicity Amplitudes: The QM Analogue of the Spontaneously Broken Case
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Decoupling A and B model in open string theory -- Topological adventures in the world of tadpoles
• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model
• Dynamical quantum phase transitions from random matrix theory
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• On the Riemann-Hilbert approach to asymptotics of tronquée solutions of Painlevé I
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle
• Symplectic cuts and open/closed strings I
• Phase space and phase transitions in the Penner matrix model with negative coupling constant
• Multi-instantons in 2d string theory
• Generalized Penner model and the Gaussian beta ensemble
• The Phases of Chaos