$1/N^2$ correction to free energy in hermitian two-matrix model

Abstract

Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for $F^1$ in hermitian one-matrix model. We discuss the relationship between $F^1$, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian over spectral curve.

References in corpus (4)

• 2D Gravity and Random Matrices
• Bihamiltonian Hierarchies in 2D Topological Field Theory At One-Loop Approximation
• Complex Curve of the Two Matrix Model and its Tau-function
• Free Energy of the Two-Matrix Model/dToda Tau-Function

Cited by in corpus (14)

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• Hermitean matrix model free energy: Feynman graph technique for all genera
• Free energy topological expansion for the 2-matrix model
• Matrix eigenvalue model: Feynman graph technique for all genera
• Algebraic methods in random matrices and enumerative geometry
• Symplectic invariants, Virasoro constraints and Givental decomposition
• Large deviations and stochastic calculus for large random matrices
• Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
• Invariants of algebraic curves and topological expansion
• Second order asymptotics for matrix models
• High order expansion of matrix models and enumeration of maps
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Strings, Integrable Systems, Geometry and Statistical Models
• Non-homogenous disks in the chain of matrices