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Combinatorics of the Modular Group II: the Kontsevich integrals

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arxiv hep-th/9201001 v1 pith:JBQU6IXX submitted 1991-12-31 hep-th math.QA

C. Itzykson , J.-B. Zuber This is my paper · ORCID
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keywords kontsevichequationexpansionfunctionsintegralsintersectiontheoremvirasoro
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We study algebraic aspects of Kontsevich integrals as generating functions for intersection theory over moduli space and review the derivation of Virasoro and KdV constraints. 1. Intersection numbers 2. The Kontsevich integral 2.1. The main theorem 2.2 Expansion of Z on characters and Schur functions 2.3 Proof of the first part of the Theorem 3. From Grassmannians to KdV 4. Matrix Airy equation and Virasoro highest weight conditions 5. Genus expansion 6. Singular behaviour and Painlev'e equation. 7. Generalization to higher degree potentials

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Cited by 2 Pith papers

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  1. Non-perturbative effects in JT gravity from KdV equations

    hep-th 2025-05 conditional novelty 6.0 of 10

    The KdV equation governing 2D topological gravity admits a one-parameter transseries; its leading nonperturbative sector reproduces known JT gravity instanton corrections and extends them to multi-instanton order.

  2. All the D-Branes of Resurgence

    hep-th 2023-01 unverdicted novelty 6.0 of 10

    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.

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