Intersection numbers of Riemann surfaces from Gaussian matrix models

TL;DR

This paper connects Gaussian matrix models with intersection numbers of moduli spaces of curves, providing insights into Witten's conjecture and the p-KdV hierarchy through a duality approach.

Contribution

It introduces a duality-based Gaussian matrix model that computes intersection numbers of moduli spaces with p-spin structures, linking matrix models to algebraic geometry.

Findings

Correlation functions yield intersection numbers of moduli spaces

Duality relates matrix models to generalized Kontsevich models

Supports Witten's conjecture on p-KdV equations

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.