Matrix Integrals and Feynman Diagrams in the Kontsevich Model

Details Matrix Integrals and Feynman Diagrams in the Kontsevich Model Matrix Integrals and Feynman Diagrams in the Kontsevich Model

2001-11-07

arxiv.org/abs/math/0111082v3

Adv.Theor.Math.Phys. 7 (2003) 525-576

Mathematics

Algebraic Geometry

52 pages; final version

Scientific paper

We review some relations occurring between the combinatorial intersection theory on the moduli spaces of stable curves and the asymptotic behavior of the 't Hooft-Kontsevich matrix integrals. In particular, we give an alternative proof of the Witten-Di Francesco-Itzykson-Zuber theorem --which expresses derivatives of the partition function of intersection numbers as matrix integrals-- using techniques based on diagrammatic calculus and combinatorial relations among intersection numbers. These techniques extend to a more general interaction potential.

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