Intersection numbers of Riemann surfaces from Gaussian matrix models

Abstract

We consider a Gaussian random matrix theory in the presence of an external matrix source. This matrix model, after duality (a simple version of the closed/open string duality), yields a generalized Kontsevich model through an appropriate tuning of the external source. The n-point correlation functions of this theory are shown to provide the intersection numbers of the moduli space of curves with a p-spin structure, n marked points and top Chern class. This sheds some light on Witten's conjecture on the relationship with the pth-KdV equation.

References in corpus (8)

• Characteristic polynomials of random matrices
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Correlations of Nearby Levels Induced by a Random Potential
• Characteristic polynomials of real symmetric random matrices
• Minimal String Theory
• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Open/Closed String Duality for Topological Gravity with Matter
• Matrix Model for Discretized Moduli Space

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