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Intersection Theory from Duality and Replica

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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.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Ecole Normale Supérieure, 24 rue Lhomond, 75231, Paris Cedex 05, France

    E. Brézin

  2. Department of Basic Sciences, University of Tokyo, Meguro-ku, Komaba, Tokyo, 153, Japan

    S. Hikami

Authors
  1. E. Brézin
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  2. S. Hikami
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Correspondence to E. Brézin.

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Communicated by M.R. Douglas

Unité Mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l’École Normale Supérieure

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Brézin, E., Hikami, S. Intersection Theory from Duality and Replica. Commun. Math. Phys. 283, 507–521 (2008). https://doi.org/10.1007/s00220-008-0519-0

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  • DOI: https://doi.org/10.1007/s00220-008-0519-0

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