Fat and Thin Emergent Geometries of Hermitian One-Matrix Models

Abstract

We use genus zero free energy functions of Hermitian matrix models to define spectral curves and their special deformations. They are special plane curves defined by formal power series with integral coefficients generalizing the Catalan numbers. This is done in two different versions, depending on two different genus expansions, and these two versions are in some sense dual to each other.

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Cited by in corpus (5)

• Emergent Geometry of Matrix Models with Even Couplings
• Grothendieck's Dessins d'Enfants in a Web of Dualities. II
• A formalism of abstract quantum field theory of summation of fat graphs
• Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of ${\overline{\mathcal{M}}}_{g,n}$
• On affine coordinates of the tau-function for open intersection numbers