Notes on Matrix Models

Abstract

In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a matrix-like fashion. We discuss the relation of matrix models to two-dimensional quantum gravity coupled to conformal matter. We provide a brief overview of a variety of more general quantum mechanical matrix models and their putative worldsheet interpretation, as well as other recent developments on large $N$ systems. We end with a discussion of open questions and future directions.

arXiv comment100 pages + appendices. Comments welcome

References in corpus (91)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• de Sitter Vacua in String Theory
• M Theory As A Matrix Model: A Conjecture
• Supersymmetry and Quantum Mechanics
• Thermodynamics of Spacetime: The Einstein Equation of State
• Comments on the Sachdev-Ye-Kitaev model
• Geometric and Renormalized Entropy in Conformal Field Theory
• Towards a derivation of holographic entanglement entropy
• 2D Gravity and Random Matrices
• A Large-N Reduced Model as Superstring
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Matrix String Theory
• Two Dimensional Gauge Theories Revisited
• Black Holes and Random Matrices
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Bekenstein-Hawking Entropy and Strange Metals
• Two and three-point functions in Liouville theory
• Critical behavior of colored tensor models in the large N limit
• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Two Dimensional QCD is a String Theory
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Analytic Continuation of Liouville Theory
• M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
• De Sitter Space and Eternity
• A Matrix Model for the Two Dimensional Black Hole
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Worldsheet Derivation of a Large N Duality
• Physics and Mathematics of Calogero particles
• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Two Dimensional QCD as a String Theory
• Matrix Model Calculations beyond the Spherical Limit
• The 1/N expansion of colored tensor models
• De Sitter Musings
• Soft matrix models and Chern-Simons partition functions
• Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity
• Micromanaging de Sitter holography
• Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline
• Exact S-Matrix for 2D String Theory
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Infrared Realization of dS${}_2$ in AdS${}_2$
• The partition function of 2d string theory
• Phase Diagram of Planar Matrix Quantum Mechanics, Tensor, and Sachdev-Ye-Kitaev Models
• Equivalence of Two Dimensional QCD and the $c=1$ Matrix Model
• One-Dimensional String Theory with Vortices as Upside-Down Matrix Oscillator
• Disordered Quivers and Cold Horizons
• Quasi-linear Stokes phenomenon for the Painlevé first equation
• De Sitter Horizons & Holographic Liquids
• Combinatorial Solution of the Two-Matrix Model
• The BFSS model on the lattice
• On some integrals over the U(N) unitary group and their large N limit
• Minimal String Theory
• Topological closed-string interpretation of Chern-Simons theory
• Loops versus Matrices - The nonperturbative aspects of noncritical string
• Spectra of Eigenstates in Fermionic Tensor Quantum Mechanics
• Entanglement entropy in two dimensional string theory
• Asymptotic Form of Zero Energy Wave Functions in Supersymmetric Matrix Models
• Two-Point String Amplitudes
• Fermionic Matrix Models
• Entropy, Entanglement and Swampland Bounds in DS/dS
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Generalized Two-Dimensional QCD
• Large Order Behaviour of 2D Gravity Coupled to $d<1$ Matter
• Free Variables and the Two Matrix Model
• Comments on D-Instantons in c<1 Strings
• Geometric Entropy of Nonrelativistic Fermions and Two Dimensional Strings
• Universality of Nonperturbative Effect in Type 0 String Theory
• Generalized multicritical one-matrix models
• Mini-BFSS in Silico
• Long String Scattering in c = 1 String Theory
• Areas and entropies in BFSS/gravity duality
• Towards non-AdS Holography via the Long String Phenomenon
• Solvable Quantum Grassmann Matrices
• Quantum Cosmology Near Two Dimensions
• Matrix model approach to minimal Liouville gravity revisited
• Grassmann Matrix Quantum Mechanics
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Bulk one-point function on disk in one-matrix model
• Entanglement entropy and the large $N$ expansion of two-dimensional Yang-Mills theory
• Large N matrices from a nonlocal spin system
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Gauged fermionic matrix quantum mechanics
• Polynomial solution of quantum Grassmann matrices
• Topological order in matrix Ising models

Cited by in corpus (20)

• Quantum Simulation for High Energy Physics
• The Virasoro Minimal String
• Three-dimensional de Sitter horizon thermodynamics
• A JT supergravity as a double-cut matrix model
• Matrix integrals $\&$ finite holography
• The complex Liouville string: the matrix integral
• $T\bar{T}$ deformation of random matrices
• The two-sphere partition function in two-dimensional quantum gravity at fixed area
• A Flow in the Forest
• The two-sphere partition function in two-dimensional quantum gravity
• Loop equations for generalised eigenvalue models
• The two-sphere partition function from timelike Liouville theory at three-loop order
• Collective field theory of gauged multi-matrix models: Integrating out off-diagonal strings
• The Phases of Chaos
• Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation
• On the planar free energy of matrix models
• Fermionic Matrix Models and Bosonization
• Optimal generalisation and learning transition in extensive-width shallow neural networks near interpolation
• A Renormalization Group Analysis of the Ising Model Coupled to Causal Dynamical Triangulations
• Statistical mechanics of extensive-width Bayesian neural networks near interpolation