Large N expansion of the 2-matrix model

Abstract

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.

41 pages, 9 figures epsf

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• BGWM as Second Constituent of Complex Matrix Model
• The Cauchy two-matrix model
• Master loop equations, free energy and correlations for the chain of matrices
• Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains
• Unitary Integrals and Related Matrix Models
• Analytic and Numerical Bootstrap for One-Matrix Model and "Unsolvable" Two-Matrix Model
• Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
• Multi-instantons in minimal string theory and in matrix integrals
• Free Energy of the Two-Matrix Model/dToda Tau-Function
• Genus one contribution to free energy in hermitian two-matrix model
• Exact 2-point function in Hermitian matrix model
• Mixed correlation functions in the 2-matrix model, and the Bethe ansatz
• Combinatorics of loop equations for branched covers of sphere
• Loop equations for the semiclassical 2-matrix model with hard edges
• 2-matrix versus complex matrix model, integrals over the unitary group as triangular integrals
• Mixed Correlation Functions of the Two-Matrix Model
• Universality of Nonperturbative Effects in c<1 Noncritical String Theory
• Conifold geometries, topological strings and multi-matrix models
• Universality in the two matrix model with a monomial quartic and a general even polynomial potential
• The complex Liouville string: the matrix integral
• The complex Liouville string: the worldsheet
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• From scalar fields on quantum spaces to blobbed topological recursion
• Matrix Models, Complex Geometry and Integrable Systems. I
• Second and Third Order Observables of the Two-Matrix Model
• On the $x$-$y$ Symmetry of Correlators in Topological Recursion via Loop Insertion Operator
• A critical phenomenon in the two-matrix model in the quartic/quadratic case
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• The $1/N$ expansion for SO(N) lattice gauge theory at strong coupling
• Gravity without averaging
• Topological expansion and boundary conditions
• The complex Liouville string: worldsheet boundaries and non-perturbative effects
• The Spectrum of FZZT Branes Beyond the Planar Limit
• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory
• FZZT Brane Relations in the Presence of Boundary Magnetic Fields
• Two-matrix model with semiclassical potentials and extended Whitham hierarchy
• Blobbed topological recursion from extended loop equations
• One-matrix differential reformulation of two-matrix models
• Bootstrap Method in Theoretical Physics
• Random Matrices, Boundaries and Branes
• Non-homogenous disks in the chain of matrices