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Intersection Theory from Duality and Replica
Authors:E Brézin  S Hikami
Institution:(1) Laboratoire de Physique Théorique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France;(2) Department of Basic Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo 153, Japan
Abstract:Kontsevich’s work on Airy matrix integrals has led to explicit results for the intersection numbers of the moduli space of curves. In this article we show that a duality between k-point functions on N × N matrices and N-point functions of k × k matrices, plus the replica method, familiar in the theory of disordered systems, allows one to recover Kontsevich’s results on the intersection numbers, and to generalize them to other models. This provides an alternative and simple way to compute intersection numbers with one marked point, and leads also to some new results. Unité Mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l’école Normale Supérieure
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