Lectures on non-perturbative effects in large N gauge theories, matrix models and strings

Abstract

In these lectures I present a review of non-perturbative instanton effects in quantum theories, with a focus on large N gauge theories and matrix models. I first consider the structure of these effects in the case of ordinary differential equations, which provide a model for more complicated theories, and I introduce in a pedagogical way some technology from resurgent analysis, like trans-series and the resurgent version of the Stokes phenomenon. After reviewing instanton effects in quantum mechanics and quantum field theory, I address general aspects of large N instantons and then present a detailed review of non-perturbative effects in matrix models. Finally, I also consider two applications of these techniques in string theory

95 pages, many figures; v2: misprints corrected, clarifications added

References in corpus (16)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Open string amplitudes and large order behavior in topological string theory
• 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
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Phase transitions, double-scaling limit, and topological strings
• Universal distribution of random matrix eigenvalues near the "birth of a cut" transition
• 2D Quantum Gravity, Matrix Models and Graph Combinatorics
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Chern-Simons theory, analytic continuation and arithmetic
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Analyticity of the Free Energy of a Closed 3-Manifold
• Universality and asymptotics of graph counting problems in nonorientable surfaces
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Effective resummation methods for an implicit resurgent function
• Phase structure and critical processes of spectral curves in large N dualities

Cited by in corpus (176)

• Advances in QED with intense background fields
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• A Primer on Resurgent Transseries and Their Asymptotics
• JT gravity as a matrix integral
• An Introduction to Resurgence, Trans-Series and Alien Calculus
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Generating Non-perturbative Physics from Perturbation Theory
• Nonperturbative Ambiguities and the Reality of Resurgent Transseries
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Quasinormal modes of black holes and Borel summation
• RG Flows and Bifurcations
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• Three-Dimensional Extended Bargmann Supergravity
• On Continuous 2-Category Symmetries and Yang-Mills Theory
• 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
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• TBA equations and resurgent Quantum Mechanics
• Direct derivation of "mirror" ABJ partition function
• 3d Modularity
• Toward Picard-Lefschetz Theory of Path Integrals, Complex Saddles and Resurgence
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
• Topological Strings and Quantum Spectral Problems
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Resumming the string perturbation series
• Nonperturbative Quantum Physics from Low-Order Perturbation Theory
• M-theoretic matrix models
• Resurgence in complex Chern-Simons theory
• Eigenvalue tunnelling and decay of quenched random networks
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• The Power of Perturbation Theory
• Fast Summation of Divergent Series and Resurgent Transseries in Quantum Field Theories from Meijer-G Approximants
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Peacock patterns and new integer invariants in topological string theory
• Normalization of D-instanton Amplitudes
• D-instantons, String Field Theory and Two Dimensional String Theory
• Holomorphic Anomaly and Quantum Mechanics
• On matrix models and their $q$-deformations
• Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
• Normalization of Type IIB D-instanton Amplitudes
• Resurgence in $\eta$-deformed Principal Chiral Models
• Multi-instantons in minimal string theory and in matrix integrals
• On exact-WKB analysis, resurgent structure, and quantization conditions
• The curious incident of multi-instantons and the necessity of Lefschetz thimbles
• Renormalons in integrable field theories
• Remark on the Dunne-Unsal relation in exact semi-classics
• Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on $S^1$
• Notes on Matrix Models
• A Solvable Deformation of Quantum Mechanics
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Resurgence and Holomorphy: From Weak to Strong Coupling
• Resurgence in the O(4) sigma model
• Exact multi-instantons in topological string theory
• Localization at large N in Chern-Simons-matter theories
• On the Higher Loop Euler-Heisenberg Trans-Series Structure
• Resurgence for superconductors
• Exact perturbative results for the Lieb-Liniger and Gaudin-Yang models
• New renormalons from analytic trans-series
• Quantum Curves, Resurgence and Exact WKB
• From perturbative to non-perturbative in the O(4) sigma model
• Exponential Networks, WKB and Topological String
• On Perturbation theory improved by Strong coupling expansion
• Resonant resurgent asymptotics from quantum field theory
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Testing the Bethe ansatz with large N renormalons
• Gradient flows without blow-up for Lefschetz thimbles
• What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles
• Cabling procedure for the colored HOMFLY polynomials
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• The full analytic trans-series in integrable field theories
• S-duality resurgence in SL(2) Chern-Simons theory
• Resurgence, Conformal Blocks, and the Sum over Geometries in Quantum Gravity
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Cutkosky Rules and Unitarity (Violation) in D-instanton Amplitudes
• Solvable Quantum Grassmann Matrices
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• Analytic resurgence in the O(4) model
• Relativistic Hydrodynamics: A Singulant Perspective
• Gibbs entropy from entanglement in electric quenches
• Interacting Thermofield Doubles and Critical Behavior in Random Regular Graphs
• Phase Transition in Tensor Models
• Resurgence and renormalons in the one-dimensional Hubbard model
• Instanton effects vs resurgence in the $O(3)$ sigma model
• Schwinger pair production from Padé-Borel reconstruction
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• JT gravity and the asymptotic Weil-Petersson volume
• Universality of the topological string at large radius and NS-brane resurgence
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• A new look at instantons and large-N limit
• A new renormalon in two dimensions
• Exact WKB analysis for $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics: Study of the Ai-Bender-Sarkar conjecture
• Instantons, renormalons and the theta angle in integrable sigma models
• Resurgence analysis of 2d Yang-Mills theory on a torus
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• The spectral problem of the ABJ Fermi gas
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Multi-cut Solutions in Chern-Simons Matrix Models
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Perturbative/nonperturbative aspects of Bloch electrons in a honeycomb lattice
• Numerical stochastic perturbation theory applied to the twisted Eguchi-Kawai model
• Rolling Near the Tachyon Vacuum
• Non-Perturbative String Theory from AdS/CFT
• Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5
• On classical and semiclassical properties of the Liouville theory with defects
• Instantons in sine-Liouville theory
• Crystals of gauged solitons, force free plasma and resurgence
• Deformed Cauchy random matrix ensembles and large $N$ phase transitions
• A resurgence analysis of the $SU(2)$ Chern-Simons partition functions on a Brieskorn homology sphere $\Sigma (2,5,7)$
• Operator thermalisation in $d>2$: Huygens or resurgence
• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• All-orders asymptotics of tensor model observables from symmetries of restricted partitions
• Instantons and Extreme Value Statistics of Random Matrices
• Resurgence of the Effective Action in Inhomogeneous Fields
• High order perturbation theory for difference equations and Borel summability of quantum mirror curves
• Renormalons in quantum mechanics
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Phase Space Distribution of Riemann Zeros
• Moduli space of supersymmetric QCD in the Veneziano limit
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
• Summing up perturbation series around superintegrable point
• Resurgent Analysis of SU(2) Chern-Simons Partition Function on Brieskorn Spheres $\Sigma (2,3,6n+5)$
• Three roads to the energy gap
• Exact instanton transseries for quantum mechanics
• Deformation of superintegrability in the Miwa-deformed Gaussian matrix model
• Reduction of Order and Transseries Structure of Radiation Reaction
• What if string theory has a de Sitter excited state?
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• Resurgence and semiclassical expansion in two-dimensional large-$N$ sigma models
• Confinement as Analytic Continuation Beyond Infinity
• The "Null-A" superintegrability for monomial matrix models
• All-order Resurgence from Complexified Path Integral in a Quantum Mechanical System with Integrability
• Dynamical quantum phase transitions from random matrix theory
• The small-$N$ series in the zero-dimensional $O(N)$ model: constructive expansions and transseries
• On the Riemann-Hilbert approach to asymptotics of tronquée solutions of Painlevé I
• Large N instantons from topological strings
• Introductory Lectures on Resurgence: CERN Summer School 2024
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
• Resurgence and $1/N$ Expansion in Integrable Field Theories
• Resurgence for the non-conformal Bjorken flow with Fermi-Dirac and Bose-Einstein statistics
• de Sitter State in Heterotic String Theory
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Large N Optimization for multi-matrix systems
• Duality Constraints on String Theory: Instantons and spectral networks
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Resurgence in complex Chern-Simons theory at generic levels
• Trans-series from condensates
• Orientation Reversal and the Chern-Simons Natural Boundary
• High energy QCD Lipatov's effective action in Euclidean space
• Bions and Instantons in Triple-well and Multi-well Potentials
• Averaging method in combinatorics of symmetric polynomials
• Perturbative structure of two- and four-point functions of color charge in a non-Gaussian small-$x$ action
• On the resummation of the Lee-Yang edge singularity coupled to gravity
• Resurgence in the Scalar Quantum Electrodynamics Euler-Heisenberg Lagrangian
• Resurgence, a problem of missing exponential corrections in asymptotic expansions
• Loop equations for generalised eigenvalue models
• Phase space and phase transitions in the Penner matrix model with negative coupling constant
• Multi-instantons in 2d string theory
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities
• Prescription for choosing an interpolating function
• Instantons and transseries of the Mathieu potential deformed by a $\mathcal{P}\mathcal{T}$-symmetry parameter
• Spectral Problems for Quasinormal Modes of Black Holes
• $c_{\mathrm{eff}}$ from Resurgence at the Stokes Line