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2007

Intersection theory from duality and replica

Brezin, E., Hikami, S.

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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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Harish-Chandra, Proc. Nat. Acad. Sci. 42
1956
Earlier work this paper cites.
C. Itzykson and J.-B. Zuber, J. Math. Phys. 21
1980
Earlier work this paper cites.
E. Witten, Surveys in Differential Geometry 1, 243 (1991)
1991
Earlier work this paper cites.
V.A. Kazakov, Nucl.Phys. B 354 ,614 (1991)
1991
Earlier work this paper cites.
M. Kontsevich, Commun. Math. Phys. 147, 1 (1992)
1992
Earlier work this paper cites.
C. Itzykson and J.-B. Zuber, Int. Journ. Mod. Phys. A7, 5661 (1992)
1992
Earlier work this paper cites.

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