The Stanford-Witten-Norbury volume recursion is shown to be directly derivable from a spectral curve that computes the Laplace transforms of the volumes using topological recursion.
Free energy topological expansion for the 2-matrix model
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abstract
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.
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UNVERDICTED 8representative citing papers
A random matrix model is built to compute the WP volumes V^{(2m)}_{g,n}({b_i}) for super-Riemann surfaces with NS boundaries and 2m R-punctures, yielding the previously missing spectral curve and closed-form expressions via topological recursion.
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
Correlators of many integrable models are specializations of universal formulae built from one defining function via KdV/Gel'fand–Dikii structure, including a new closed form for V_{4,n}.
Schwinger-Dyson equations for 2D Euclidean pure gravity are reformulated as Chekhov-Eynard-Orantin topological recursion for basic-type, strip-type, and continuum dynamical triangulation models.
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
Topological recursion solves Schwinger-Dyson equations for multicritical and causal dynamical triangulations in 2D quantum gravity, yielding explicit amplitudes.
Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.
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$c=1$ strings as a matrix integral
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.