Combinatorics of the Modular Group II: the Kontsevich integrals

Details Combinatorics of the Modular Group II: the Kontsevich integrals Combinatorics of the Modular Group II: the Kontsevich integrals

1991-12-31

arxiv.org/abs/hep-th/9201001v1

Int.J.Mod.Phys. A7 (1992) 5661-5705

Physics

High Energy Physics

High Energy Physics - Theory

46 pages

Scientific paper

10.1142/S0217751X92002581

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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