Les Houches lectures on matrix models and topological strings

Abstract

In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model technology and then we focus on type B topological strings. We present the main results of Dijkgraaf and Vafa describing the spacetime string dynamics on certain Calabi-Yau backgrounds in terms of matrix models, and we emphasize the connection to geometric transitions and to large N gauge/string duality. We also use matrix model technology to analyze large N Chern-Simons theory and the Gopakumar-Vafa transition.

63 pages, 8 figures, minor corrections

References in corpus (31)

• Large N Field Theories, String Theory and Gravity
• Mirror Manifolds And Topological Field Theory
• A Perturbative Window into Non-Perturbative Physics
• All genus correlation functions for the hermitian 1-matrix model
• D-Branes on Calabi-Yau Spaces and Their Mirrors
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Disk Instantons, Mirror Symmetry and the Duality Web
• Worldsheet Derivation of a Large N Duality
• Open string instantons and superpotentials
• Chern-Simons Theory and Topological Strings
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Gravitational corrections in supersymmetric gauge theory and matrix models
• Soft matrix models and Chern-Simons partition functions
• Perturbative Analysis of Gauged Matrix Models
• Conformal Matrix Models as an Alternative to Conventional Multi-Matrix Models
• The Topological CP^1 Model and the Large-N Matrix Integral
• Geometric Transitions and N=1 Quiver Theories
• Character Expansion Methods for Matrix Models of Dually Weighted Graphs
• D-brane effective field theory from string field theory
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Topological Matter in Two Dimensions
• Conformal Field Theory Techniques in Random Matrix models
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory
• The Topological Matrix Model Of c=1 String
• A Generating Function for Fatgraphs
• 2D Quantum Gravity, Matrix Models and Graph Combinatorics
• Type B Topological Matter, Kodaira-Spencer Theory, and Mirror Symmetry
• Chern-Simons Matrix Models and Unoriented Strings
• Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques
• Chern-Simons matrix model for local conifold

Cited by in corpus (89)

• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• Open string amplitudes and large order behavior in topological string theory
• JT gravity as a matrix integral
• Refined Topological Vertex and Instanton Counting
• Holomorphic anomaly and matrix models
• $N^3$-behavior from 5D Yang-Mills theory
• Quantum Dynamics in Krylov Space: Methods and Applications
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds
• Algebraic methods in random matrices and enumerative geometry
• 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
• Multi-Instantons and Multi-Cuts
• Exact results for Wilson loops in arbitrary representations
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• A mini-course on topological strings
• From Matrix Models and quantum fields to Hurwitz space and the absolute Galois group
• The uses of the refined matrix model recursion
• Phase transitions, double-scaling limit, and topological strings
• Phase transitions in q-deformed 2d Yang-Mills theory and topological strings
• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Interacting fermions and N=2 Chern-Simons-matter theories
• Free Fermions and Thermal AdS/CFT
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
• Finite N from Resurgent Large N
• Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
• Global Properties of Topological String Amplitudes and Orbifold Invariants
• What is the Simplest Gauge-String Duality?
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• Exact probes of orientifolds
• Supersymmetric $U(N)$ Chern-Simons-matter theory and phase transitions
• Large N phase transitions in supersymmetric Chern-Simons theory with massive matter
• A DK Phase Transition in q-Deformed Yang-Mills on S^2 and Topological Strings
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Non-perturbative effects and wall-crossing from topological strings
• Black-holes, topological strings and large N phase transitions
• Lectures on Mirror Symmetry and Topological String Theory
• Super-quantum curves from super-eigenvalue models
• Conifold geometries, topological strings and multi-matrix models
• A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory
• Quantum curves and conformal field theory
• Non-compact Topological Branes on Conifold
• The Hilbert series of U/SU SQCD and Toeplitz Determinants
• D-Brane Amplitudes in Topological String on Conifold
• Universality and asymptotics of graph counting problems in nonorientable surfaces
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Factorising the 3D Topologically Twisted Index
• Flowing in discrete gravity models and Ward identities: A review
• Chern-Simons Theory on Seifert Manifold and Matrix Model
• A Macdonald refined topological vertex
• Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process
• On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories
• Emergent Phase Space Description of Unitary Matrix Model
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Topological B-model and $\hat{c}=1$ String Theory
• Holomorphic Couplings In Non-Perturbative String Compactifications
• Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels
• Topological String Correlators from Matrix Models
• The topological open string wavefunction
• Deformed Cauchy random matrix ensembles and large $N$ phase transitions
• Double Scaling Limits in Gauge Theories and Matrix Models
• Instantons and Extreme Value Statistics of Random Matrices
• Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
• A Large N expansion for Gravity
• Conifold geometries, matrix models and quantum solutions
• Phase Space Distribution of Riemann Zeros
• Phase Space Distribution for Two-Gap Solution in Unitary Matrix Model
• Moduli space of supersymmetric QCD in the Veneziano limit
• Introduction to Monte Carlo for Matrix Models
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• Flavour from partially resolved singularities
• Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• Geometric transitions, double scaling limits and gauge theories
• Large N instantons from topological strings
• Black holes and balanced metrics
• Gas of baby universes in JT gravity and matrix models
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Stochastic analysis & discrete quantum systems
• Doubled Formalism, Complexification and Topological Sigma-Models
• Scattering and Strebel graphs
• Some comments on the local curve (B-side)
• A Matrix model from string field theory
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Lattice random walks and quantum A-period conjecture
• Quantum chaos in 2D gravity
• Equivariant and supersymmetric localization in QFT
• On the planar free energy of matrix models