Matrix models and a proof of the open analog of Witten's conjecture

TL;DR

This paper proves the open KdV conjecture for intersection theory on moduli spaces of Riemann surfaces with boundary, using matrix models and a combinatorial formula.

Contribution

It provides a proof of the open KdV conjecture by connecting matrix models with intersection theory on moduli spaces with boundary.

Findings

Confirmed the open KdV equations for boundary moduli spaces

Developed a Kontsevich type combinatorial formula for intersection numbers

Established a matrix model approach to open intersection theory

Abstract

In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers satisfies the open KdV equations. In this paper we prove this conjecture. Our proof goes through a matrix model and is based on a Kontsevich type combinatorial formula for the intersection numbers that was found by the second author.