Combinatorics of the Modular Group II: the Kontsevich integrals
High Energy Physics - Theory
2016-09-06 v1 Quantum Algebra
Abstract
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
Keywords
Cite
@article{arxiv.hep-th/9201001,
title = {Combinatorics of the Modular Group II: the Kontsevich integrals},
author = {C. Itzykson and J. -B. Zuber},
journal= {arXiv preprint arXiv:hep-th/9201001},
year = {2016}
}
Comments
46 pages