Intersection theory from duality and replica

Details Intersection theory from duality and replica Intersection theory from duality and replica

2007-08-16

arxiv.org/abs/0708.2210v1

Commun.Math.Phys.283:507-521,2008

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1007/s00220-008-0519-0

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 $N\times N$ matrices and N-point functions of $k\times k$ 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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