Correlators of diverse models are expressed via universal formulae derived from a single defining function using KdV flows and the Gel'fand-Dikii equation.
Free energy topological expansion for the 2-matrix model
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
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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representative citing papers
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.