2D Gravity and Random Matrices

Abstract

We review recent progress in 2D gravity coupled to $d<1$ conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related $O(n)$ matrix models. For $d<1$ matter, the matrix problem can be completely solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively, in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representations of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising--like matter, the sum over topologies is reduced to the solution of non-linear differential equations (the Painlevé equation in the pure gravity case) which can be shown to follow from an action principle. In the case of pure gravity and more generally all unitary models, the perturbation theory is not Borel summable and therefore alone does not define a unique solution. In the non-Borel summable case, the matrix model does not define the sum over topologies beyond perturbation theory. We also review the computation of correlation functions directly in the continuum formulation of matter coupled to 2D gravity, and compare with the matrix model results. Finally, we review the relation between matrix models and topological gravity, and as well the relation to intersection theory of the moduli space of punctured Riemann surfaces.

190 pages (harvmac l mode), 400kb (don't even dream of requesting hardcopy)

References in corpus (12)

• Towards unified theory of $2d$ gravity
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• Multicritical Phases of the O(n) Model on a Random Lattice
• The $O(n)$ model on a random surface: critical points and large order behaviour
• Ground Rings and Their Modules in 2D Gravity with $c\le 1$ Matter
• Polynomial averages in the Kontsevich model
• From Virasoro Constraints in Kontsevich's Model to $\mathcal{W}$-constraints in 2-matrix Models
• Large Order Behaviour of 2D Gravity Coupled to $d<1$ Matter
• Open String Theory in 1+1 Dimensions
• On the Liouville Approach to Correlation Functions for 2-D Quantum Gravity
• Scattering of Open and Closed Strings in 1+1 Dimensions

Cited by in corpus (641)

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• Lectures on non-perturbative effects in large N gauge theories, matrix models and strings
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• Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
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• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
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• Emergent Models for Gravity: an Overview of Microscopic Models
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• Invitation to Random Tensors
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• Infinite Products of Large Random Matrices and Matrix-valued Diffusion
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• Resurgent Extrapolation: Rebuilding a Function from Asymptotic Data. Painleve I
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• On the finite amplitudes for open graphs in Abelian dynamical colored Boulatov-Ooguri models
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Renormalization of the noncommutative phi^3 model through the Kontsevich model
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Universal distribution of random matrix eigenvalues near the "birth of a cut" transition
• Fermionic Matrix Models
• Chiral random matrix theory for two-color QCD at high density
• Compact support probability distributions in random matrix theory
• Matrix ensembles with global symmetries and 't Hooft anomalies from 2d gauge theory
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Beta functions of $U(1{)}^d$ gauge invariant just renormalizable tensor models
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• From operator statistics to wormholes
• Singular Vertices and the Triangulation Space of the D-sphere
• Entanglement Typicality
• A recursive approach to the O(n) model on random maps via nested loops
• Comments on Effective Superpotentials via Matrix Models
• Sum rules for characters from character-preservation property of matrix models
• Matrix Models and Deformations of JT Gravity
• Random Tensors and Quantum Gravity
• Bubbles and jackets: new scaling bounds in topological group field theories
• Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
• Sphere and disk partition functions in Liouville and in matrix integrals
• Multi-instantons in minimal string theory and in matrix integrals
• The three-point function of planar quadrangulations
• Distance statistics in quadrangulations with a boundary, or with a self-avoiding loop
• Matrix Model Combinatorics: Applications to Folding and Coloring
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Random Levy Matrices Revisited
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• Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence
• Equivariant Localization of Path Integrals
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• Random matrix models with log-singular level confinement: method of fictitious fermions
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Notes on Matrix Models
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• Genus one contribution to free energy in hermitian two-matrix model
• Exact 2-point function in Hermitian matrix model
• Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups
• Multi-critical behaviour of 4-dimensional tensor models up to order 6
• Constructive tensor field theory: The $T_4^4$ model
• Relational evolution of effectively interacting GFT quantum gravity condensates
• A JT supergravity as a double-cut matrix model
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Alpha states demystified: Towards microscopic models of AdS${}_2$ holography
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• Normalization of ZZ instanton amplitudes in minimal string theory
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• An analysis of the intermediate field theory of $T^4$ tensor model
• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• Boundary Ground Ring in 2D String Theory
• The ZZ annulus one-point function in non-critical string theory: A string field theory analysis
• Adding flavor to Dijkgraaf-Vafa
• Exact probes of orientifolds
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Inhomogeneous universe from group field theory condensate
• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
• The dynamic exponent of the Ising model on negatively curved surfaces
• Second order asymptotics for matrix models
• Random matrix model approach to chiral symmetry
• Bilinear semi-classical moment functionals and their integral representation
• Mixed correlation functions in the 2-matrix model, and the Bethe ansatz
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Coupling of hard dimers to dynamical lattices via random tensors
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Blocked edges on Eulerian maps and mobiles: Application to spanning trees, hard particles and the Ising model
• Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions
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• Correlators in the Simplest Gauge-String Duality
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• 3D Field Theories with Chern--Simons Term for Large $N$ in the Weyl Gauge
• Rational differential systems, loop equations, and application to the q-th reductions of KP
• Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Invariant Integration over the Unitary Group
• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
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• Isomonodromic Properties of the Seiberg-Witten Solution
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• $q$-Virasoro modular double and 3d partition functions
• Generating series for GUE correlators
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• Cosmological evolution as squeezing: a toy model for group field cosmology
• The transfer matrix in four-dimensional CDT
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• The Complete Barrett-Crane Model and its Causal Structure
• JT Gravity Limit of Liouville CFT and Matrix Model
• Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model
• Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity
• Critical and Multicritical Semi-Random (1+d)-Dimensional Lattices and Hard Objects in d Dimensions
• Asymptotics of skew orthogonal polynomials
• A semiclassical matrix model for quantum chaotic transport
• Asymptotics for the partition function in two-cut random matrix models
• Symmetry breaking in tensor models
• Quantum Curve and the First Painlevé Equation
• Correlators for the Wigner-Smith time-delay matrix of chaotic cavities
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies
• A Real-Space Renormalization Group for Random Surfaces
• The multicomponent 2D Toda hierarchy: dispersionless limit
• The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CP^n
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Statistics of planar graphs viewed from a vertex: A study via labeled trees
• An Analytical Analysis of CDT Coupled to Dimer-like Matter
• $1/N^2$ correction to free energy in hermitian two-matrix model
• An action for the exact string black hole
• Random Matrix Model for Superconductors in a Magnetic Field
• Coloring Random Triangulations
• Towards background independent quantum gravity with tensor models
• On the Chemical Potential of D-instantons in c=0 Noncritical String Theory
• Boundary correlation numbers in one matrix model
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Minimal Open Strings
• Rotational Symmetry Breaking in Multi-Matrix Models
• Generalized multicritical one-matrix models
• A prediction for bubbling geometries
• Geometrically constrained statistical systems on regular and random lattices: From folding to meanders
• Statistics of geodesics in large quadrangulations
• Matrix integrals $\&$ finite holography
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• The full Ward-Takahashi Identity for colored tensor models
• Planar maps and continued fractions
• Inverse scattering method and vector higher order nonlinear Schrodinger equation
• Random Matrices and Random Permutations
• N=4 Super NLS-mKdV Hierarchies
• 2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
• Ising Spins on a Gravitating Sphere
• The PDEs of biorthogonal polynomials arising in the two-matrix model
• Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models
• Determination of S-curves with applications to the theory of nonhermitian orthogonal polynomials
• Integrable flows in c=1 string theory
• (No) phase transition in tensorial group field theory
• Loop equations for the semiclassical 2-matrix model with hard edges
• Two Ising Models Coupled to 2-Dimensional Gravity
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• Mixed Correlation Functions of the Two-Matrix Model
• Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity
• HCIZ integral and 2D Toda lattice hierarchy
• Phases of planar 5-dimensional supersymmetric Chern-Simons theory
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Tensor and Matrix models: a one-night stand or a lifetime romance?
• Combinatorics of bicubic maps with hard particles
• Integrability in SFT and new representation of KP tau-function
• Taming the cosmological constant in 2D causal quantum gravity with topology change
• A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions
• Open/Closed String Duality for Topological Gravity with Matter
• The KP Hierarchy in Miwa Coordinates
• Quantum curves and conformal field theory
• Higher order loop equations for A_r and D_r quiver matrix models
• The partition function of the two-matrix model as an isomonodromic tau-function
• Conifold geometries, topological strings and multi-matrix models
• A Matrix model for plane partitions
• Geodesic distances in Liouville quantum gravity
• Universality in the two matrix model with a monomial quartic and a general even polynomial potential
• Phase Transition in Tensor Models
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Lie 2-algebra models
• Comments on the Quantum Field Theory of the Coulomb Gas Formalism
• Solution of all quartic matrix models
• Generating functions for intersection numbers on moduli spaces of curves
• Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painleve I transcendent
• Purity distribution for generalized random Bures mixed states
• Notes on the algebraic curves in (p,q) minimal string theory
• Nonperturbative Effect in c=1 Noncritical String Theory and Penner Model
• On the Large N Limit of 3D and 4D Hermitian Matrix Models
• Scattered Results in 2D String Theory
• The complex Liouville string: the matrix integral
• Minimal Superstrings and Loop Gas Models
• Higher Order Analogues of Tracy-Widom Distributions via the Lax Method
• Exact amplitudes in four dimensional non-critical string theories
• Theory of random matrices with strong level confinement: orthogonal polynomial approach
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Emergent gravitational dynamics from multi-BEC hydrodynamics?
• Counting Colored Random Triangulations
• Simple maps, Hurwitz numbers, and Topological Recursion
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Hints of unitarity at large $N$ in the $O(N{)}^3$ tensor field theory
• Convergence from Divergence
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• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Reliability of the local truncations for the random tensor models renormalization group flow
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• Combinatorics of Hard Particles on Planar Graphs
• Geometrical optics in nonlinear media and integrable equations
• The complex Liouville string: the worldsheet
• Mixed correlation function and spectral curve for the 2-matrix model
• Wilsonian Approximated Renormalization Group for Matrix and Vector Models in 2<d<4
• On the large N limit of matrix integrals over the orthogonal group
• The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
• Integrable differential systems of topological type and reconstruction by the topological recursion
• A Celestial Matrix Model
• Exact solution of matricial ${\Phi }_2^3$ quantum field theory
• Explicit factorization of Seiberg-Witten curves with matter from random matrix models
• Frozen formalism and canonical quantization in group field theory
• Partition functions and the continuum limit in Penner matrix models
• Operator growth bounds in a cartoon matrix model
• Second and Third Order Observables of the Two-Matrix Model
• Virasoro Constraints and Flavor-Topology Duality in QCD
• Flowing in discrete gravity models and Ward identities: A review
• On the large $D$ expansion of Hermitian multi-matrix models
• Solving the Frustrated Spherical Model with q-Polynomials
• $T\bar{T}$ deformation of random matrices
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Spectral dimension of Liouville quantum gravity
• Statistical mechanics of graph models and their implications for emergent spacetime manifolds
• Iterative Solution of the Supereigenvalue Model
• Boundary operators in minimal Liouville gravity and matrix models
• A random matrix model with non-pairwise contracted indices
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Simple matrix models for random Bergman metrics
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• Two-dimensional state sum models and spin structures
• A unified fluctuation formula for one-cut $\beta$-ensembles of random matrices
• Topological expansion of the chain of matrices
• Exact equivalences and phase discrepancies between random matrix ensembles
• A Solvable Model of Flat Space Holography
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Vortices in a cylinder: Localization after depinning
• The Hausdorff Dimension of Surfaces in Two-Dimensional Quantum Gravity Coupled to Ising Minimal Matter
• Fine structure in the large n limit of the non-hermitian Penner matrix model
• Random volumes from matrices
• Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach
• SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings
• Extending the Tutte and Bollobás-Riordan Polynomials to Rank 3 Weakly-Colored Stranded Graphs
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Non-critical strings at high energy
• Multiple phases and meromorphic deformations of unitary matrix models
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• A concise expression for the ODE's of orthogonal polynomials
• From Noncommutative Geometry to Random Matrix Theory
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Bulk one-point function on disk in one-matrix model
• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Comments on Quiver Gauge Theories and Matrix Models
• Boundary transitions of the O(n) model on a dynamical lattice
• Higher Equations of Motion in Boundary Liouville Field Theory
• Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations
• On tau-functions for the Toda lattice hierarchy
• Nonperturbative Model Of Liouville Gravity
• Yang-Lee Zeros of the Ising model on Random Graphs of Non Planar Topology
• Convergence of Combinatorial Gravity
• A note on the integral equation for the Wilson loop in N = 2 D=4 superconformal Yang-Mills theory
• Gravity without averaging
• New Critical Matrix Models and Generalized Universality
• A matrix model for the topological string II: The spectral curve and mirror geometry
• Sparse random matrices and Gaussian ensembles with varying randomness
• Topological B-model and $\hat{c}=1$ String Theory
• Emergence of order in random languages
• Melonic Turbulence
• Spontaneous Symmetry Breaking in Tensor Theories
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• Nesting statistics in the O(n) loop model on random planar maps
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• The double scaling limit method in the Toda hierarchy
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
• On the singular sector of the Hermitian random matrix model in the large N limit
• Deformed Cauchy random matrix ensembles and large $N$ phase transitions
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• Nonlinear Random Matrix Statistics, symmetric functions and hyperdeterminants
• Five-point Correlation Numbers in One-Matrix Model
• N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model
• A model of quantum gravity with emergent spacetime
• Supereigenvalue Models and Topological Recursion
• Confluence of geodesic paths and separating loops in large planar quadrangulations
• Fermionic Quantum Gravity
• Random vector and matrix and vector theories: a renormalization group approach
• Large N gauge theories and topological cigars
• Double Scaling Limits in Gauge Theories and Matrix Models
• Topological Recursion in The Ramond Sector
• Topological expansion and boundary conditions
• Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
• Surgery in colored tensor models
• A Renormalizable SYK-type Tensor Field Theory
• Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks
• On the plane into plane mappings of hydrodynamic type. Parabolic case
• Numerical and analytical analyses of a matrix model with non-pairwise contracted indices
• Instantons and Extreme Value Statistics of Random Matrices
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• The asymmetric ABAB matrix model
• Geometry of the basic statistical physics mapping
• Site Percolation on Planar ${\Phi }^3$ Random Graphs
• A remark on the three approaches to 2D Quantum gravity
• Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
• String Theory and Water Waves
• Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model
• Spin/disorder correlations and duality in the c=1/2 string
• Exact Solutions of Integrable 2D Contour Dynamics
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Faces of matrix models
• PT-symmetric interpretation of double-scaling
• Average characteristic polynomials in the two-matrix model
• Double Scaling Limits and Twisted Non-Critical Superstrings
• A Review of Symmetry Algebras of Quantum Matrix Models in the Large-N Limit
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• String modes, propagators and loops on fuzzy spaces
• A Collection of Exercises in Two-Dimensional Physics, Part 1
• Spheres are rare
• Double scaling limit of multi-matrix models at large $D$
• Stochastic Laplacian growth
• Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space
• Semi-Classical Mechanics in Phase Space: The Quantum Target of Minimal Strings
• Double scaling limit of the prismatic tensor model
• Five-point correlation numbers in minimal Liouville gravity and matrix models
• On Itzykson-Zuber Ansatz
• Matter fields in triangle-hinge models
• Non-perturbative double scaling limits
• Four-point function in Super Liouville Gravity
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• Improved matrix-model calculation of the N=2 prepotential
• Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
• The Chiral Supereigenvalue Model
• Stochastic dynamics for Group Field Theories
• From $r$-Spin Intersection Numbers to Hodge Integrals
• On Connected Diagrams and Cumulants of Erdos-Renyi Matrix Models
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Invariant and Group Theoretical Integrations over the U(n) Group
• $(D+1)$-Colored Graphs - a Review of Sundry Properties
• Minisuperspace computation of the Mabuchi spectrum
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
• 3D $\mathcal{N}=1$ supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
• Introduction to Monte Carlo for Matrix Models
• Wilson loops and its correlators with chiral operators in $\mathcal{N}=2,4$ SCFT at large $N$
• A Simple Approach to Global Regime of the Random Matrix Theory
• Curvature effects in the spectral dimension of spin foams
• Integrability of graph combinatorics via random walks and heaps of dimers
• Generic critical points of normal matrix ensembles
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• Sextic tensor model in rank $3$ at next-to-leading order
• Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula
• Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory
• A new type of critical behaviour in random matrix models
• Non-probabilistic fermionic limit shapes
• Genus expansion of open free energy in 2d topological gravity
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• Note on large-$p$ limit of $(2,2p+1)$ minimal Liouville gravity and moduli space volumes
• Double scaling limits of Dirac ensembles and Liouville quantum gravity
• Baby universes in 2d and 4d theories of quantum gravity
• Two-matrix model with semiclassical potentials and extended Whitham hierarchy
• On Exact Superpotentials, Free Energies and Matrix Models
• Relational dynamics and Page-Wootters formalism in group field theory
• Solving matrix models using holomorphy
• Quantum Gravity as a Multitrace Matrix Model
• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model
• Geometry in transition in four dimensions: A model of emergent geometry in the early universe and dark energy
• Exactly solvable models for 2D correlated fermions
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• The Critical Exponents Of The Matrix Valued Gross-Neveu Model
• A Lagrangean formalism for Hermitean matrix models
• N = 2 Super $W_{\infty }$ Algebra and its Nonlinear Realization Through Super KP Formulation
• Semiclassical Partition Functions for Gravity with Cosmic Strings
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• BPS states, crystals and matrices
• Boundary operators in the one-matrix model
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• An $OSp$ extension of Canonical Tensor Model
• Blobbed topological recursion for the quartic melonic tensor model
• A Recipe for Constructing Frustration-Free Hamiltonians with Gauge and Matter Fields in One and Two Dimensions
• Probability around the Quantum Gravity. Part 1: Pure Planar Gravity
• Fermions in the harmonic potential and string theory
• Noise Effects on Pade Approximants and Conformal Maps
• A Diagrammatic Equation for Oriented Planar Graphs
• New recursive residue formulas for the topological expansion of the Cauchy Matrix Model
• On the Riemann-Hilbert approach to asymptotics of tronquée solutions of Painlevé I
• The small-$N$ series in the zero-dimensional $O(N)$ model: constructive expansions and transseries
• Light-cone limits of large rectangular fishnets
• Open/closed duality for FZZT branes in c=1
• A Flow in the Forest
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• N=4 Sugawara construction on affine sl(2|1), sl(3) and mKdV-type superhierarchies
• Supersymmetric matrix models and branched polymers
• Dynamical quantum phase transitions from random matrix theory
• Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations
• The tensor Harish-Chandra-Itzykson-Zuber integral I: Weingarten calculus and a generalization of monotone Hurwitz numbers
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• Critical Behaviour of Spanning Forests on Random Planar Graphs
• Random manifolds and quantum gravity
• On the Yang-Lee and Langer singularities in the O(n) loop model
• Robust quantum metrology with random Majorana constellations
• Breakdown of Universality in Random Matrix Models
• Asymptotically Free AdS3/CFT2
• Hilbert space formalisms for group field theory
• A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces
• Flat histogram Monte Carlo simulations of triangulated fixed-connectivity surface models
• String bit models of two-dimensional quantum gravity coupled with matter
• Division Algebras and Extended N=2,4,8 SuperKdVs
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Multicritical Matrix-Vector Models of Quantum Orbifold Geometry
• Random matrices in non-confining potentials
• Genus expansion of matrix models and $\hslash$ expansion of $B$KP hierarchy
• Noncommutative probability, matrix models, and quantum orbifold geometry
• Quasi-classical DBAR-dressing approach to the weakly dispersive KP hierarchy
• Large N and Bethe ansatz
• Potts model coupled to causal triangulations
• Weighting bubbles in group field theory
• Duality of O(N) and Sp(N) random tensor models: tensors with symmetries
• On Inhomogeneity of a String Bit Model for Quantum Gravity
• Perturbed generalized multicritical one-matrix models
• On a class of elliptic orthogonal polynomials and their integrability
• Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions
• Integrability and Symmetry Algebra Associated with N=2 KP Flows
• Phase transitions and random matrices
• Unitary matrix integrals, symmetric polynomials, and long-range random walks
• Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
• Phase profile of the wave function of canonical tensor model and emergence of large spacetimes
• Large N expansions and Painlevé hierarchies in the Hermitian matrix model
• Backgrounds from Tensor Models: A Proposal
• Perturbative approach to the critical behaviour of two-matrix models in the limit N -> infinity
• Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model
• Spectral curves in gauge/string dualities: integrability, singular sectors and regularization
• Emergent Kalb-Ramond fields from a dimer model
• Hopf Algebras and Topological Recursion
• Topological Gravity with Non-Compact Matter
• Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Boundary States of the Potts Model on Random Planar Maps
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Stochastic melonic kinetics with random initial conditions
• Robustness of planar random graphs to targeted attacks
• Cosmological implications of the hydrodynamical phase of group field theory
• A Toy Model of Closed String Tachyon Effective Action
• Phase space and phase transitions in the Penner matrix model with negative coupling constant
• Functional renormalization group for $p=2$ like glassy matrices in the planar approximation: II. Ward identities method in the deep IR
• Integrable hierarchies in Donaldson-Witten and Seiberg-Witten theories
• Functional Renormalization Group Approach for Signal Detection
• Distance statistics in large toroidal maps
• The factorial growth of topological recursion
• Functional renormalization group for p=2 like glassy matrices in the planar approximation: I. Vertex expansion at equilibrium
• A Duality in Two-Dimensional Gravity
• Singular topologies in the Boulatov model
• Symmetric Sextic Freud Weight
• Super-Affine Hierarchies and their Poisson Embeddings
• Loop equations for generalised eigenvalue models
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• From Dimensional Reduction of 4d Spin Foam Model to Adding Non-Gravitational Fields to 3d Spin Foam Model
• Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling
• On the planar free energy of matrix models
• The finite and large-$N$ behaviors of independent-value matrix models
• Random Matrix Theory by the Supersymmetry Method Beyond the Sigma-Model
• Topological Open/Closed String Dualities: Matrix Models and Wave Functions
• The Phases of Chaos
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes
• Proof of the Lagrangean formalism of Hermitean 1-matrix models to all orders
• On the Counting of Colored Tangles
• Torus one-point correlation numbers in minimal Liouville gravity
• Landau Theory of Causal Dynamical Triangulations
• Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics
• Exact Solutions v.s. Perturbative Calculations of Finite ${\Phi }^3$-${\Phi }^4$ Hybrid-Matrix-Model
• An Exact Bosonization Rule for c=1 Noncritical String Theory
• Comments on Large N Matrix Model
• A Quantization of the Loday-Ronco Hopf Algebra
• Eigenvalue Dynamics and the Matrix Chain
• Monte Carlo Renormalization of 2d Simplicial Quantum Gravity Coupled to Gaussian Matter
• A new class of Matrix Models arising from the W-infinity Algebra
• Asymptotic Properties of a Special Solution to the (3,4) String Equation
• Higher-order heat equation and the Gelfand-Dickey hierarchy
• Susy Hierarchies and Affine Algebras
• Branched polymers, complex spins and the freezing transition
• Lie-Algebraic Characterization of 2D (Super-)Integrable Models
• A Renormalization Group Analysis of the Ising Model Coupled to Causal Dynamical Triangulations
• N=4 supersymmetric integrable systems
• Fusion rules and macroscopic loops from discretized approach to two-dimensional gravity
• Wronskians, dualities and FZZT-Cardy branes
• Dynamic Space Filling
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Non-critical string, Liouville theory and geometric bootstrap hypothesis
• Multicritical continuous random trees
• Maps of unfixed genus and blossoming trees
• Analytical approaches to 2D CDT coupled to matter
• Sums of Random Matrices and the Potts Model on Random Planar Maps
• Gravitational lensing by eigenvalue distributions of random matrix models