Topological expansion of the chain of matrices

Abstract

We solve the loop equations to all orders in $1/N^2$, for the Chain of Matrices matrix model (with possibly an external field coupled to the last matrix of the chain). We show that the topological expansion of the free energy, is, like for the 1 and 2-matrix model, given by the symplectic invariants of the associated spectral curve. As a consequence, we find the double scaling limit explicitly, and we discuss modular properties, large $N$ asymptotics. We also briefly discuss the limit of an infinite chain of matrices (matrix quantum mechanics).

23 pages, LateX

References in corpus (4)

• Free energy topological expansion for the 2-matrix model
• Holomorphic anomaly and matrix models
• Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence
• Two-matrix model with semiclassical potentials and extended Whitham hierarchy

Cited by in corpus (7)

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• The matrix model for hypergeometric Hurwitz numbers
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• Supermatrix models, loop equations, and duality
• Spectral curves for hypergeometric Hurwitz numbers
• Non-homogenous disks in the chain of matrices