The intersection numbers of the p-spin curves from random matrix theory

TL;DR

This paper computes intersection numbers of p-spin curves using Gaussian random matrix ensembles, explores their polynomial p-dependence, large p behavior, and discusses their analytic continuation related to black hole sigma models.

Contribution

It introduces a novel method linking random matrix correlation functions to p-spin intersection numbers and analyzes their behavior across different p values.

Findings

Intersection numbers are polynomial in p.

Large p asymptotic behavior characterized.

Analytic continuation relates to SL(2,R)/U(1) black hole models.

Abstract

The intersection numbers of p-spin curves are computed through correlation functions of Gaussian ensembles of random matrices in an external matrix source. The p-dependence of intersection numbers is determined as polynomial in p; the large p behavior is also considered. The analytic continuation of intersection numbers to negative values of p is discussed in relation to SL(2,R)/U(1) black hole sigma model.