Intersection Theory, Integrable Hierarchies and Topological Field Theory

Details Intersection Theory, Integrable Hierarchies and Topological Field Theory Intersection Theory, Integrable Hierarchies and Topological Field Theory

1992-01-02

arxiv.org/abs/hep-th/9201003v1

Physics

High Energy Physics

High Energy Physics - Theory

73 pages, most figures are not included. Lectures given at the Cargese Summer School on `New Symmetry Principles in Quantum Fi

Scientific paper

In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological quantum field theories. We explain in particular why matrix integrals of the type considered by Kontsevich naturally appear as tau-functions associated to minimal models. Our starting point is the extremely simple form of the string equation for the topological (p,1) models, where the so-called Baker-Akhiezer function is given by a (generalized) Airy function.

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