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Communications in Mathematical Physics

, Volume 283, Issue 2, pp 507–521 | Cite as

Intersection Theory from Duality and Replica

  • E. Brézin
  • S. Hikami
Article

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.

Keywords

Modulus Space Marked Point Intersection Number Intersection Theory Airy Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Laboratoire de Physique ThéoriqueEcole Normale SupérieureParis Cedex 05France
  2. 2.Department of Basic SciencesUniversity of TokyoTokyoJapan

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