Advances in Theoretical and Mathematical Physics

Matrix Integrals and Feynman Diagrams in the Kontsevich Model

Domenico Fiorenza and Riccardo Murri

Abstract

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.

Article information

Source
Adv. Theor. Math. Phys., Volume 7, Number 3 (2003), 525-576.

Dates
First available in Project Euclid: 4 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1112627377

Mathematical Reviews number (MathSciNet)
MR2030059

Zentralblatt MATH identifier
1047.81060

Citation

Fiorenza, Domenico; Murri, Riccardo. Matrix Integrals and Feynman Diagrams in the Kontsevich Model. Adv. Theor. Math. Phys. 7 (2003), no. 3, 525--576. https://projecteuclid.org/euclid.atmp/1112627377


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