1992/01/02 by Robbert Dijkgraaf, Dijkgraaf, Robbert
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9201003
73 pages, most figures are not included. Lectures given at the Cargese Summer School on `New Symmetry Principles in Quantum Field Theory,' July 16-27, 1991.
arxiv created 1992/01/02 · arxiv updated 2009/11/30
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.