Open intersection numbers, matrix models and MKP hierarchy

TL;DR

This paper conjectures that the generating function for open intersection numbers is a tau-function of the KP hierarchy, represented by a modified Kontsevich matrix integral, linking open and closed cases via the MKP hierarchy.

Contribution

It introduces a conjecture connecting open intersection numbers to KP and MKP integrable hierarchies through a modified matrix integral representation.

Findings

Proposes that the generating function is a KP tau-function.

Shows that open intersection numbers satisfy Virasoro constraints.

Links open and closed intersection numbers via the MKP hierarchy.

Abstract

In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a tau-function of the KP integrable hierarchy. Moreover, it is given by a simple modification of the Kontsevich matrix integral so that the generating functions of open and closed intersection numbers are described by the MKP integrable hierarchy. Virasoro constraints for the open intersection numbers naturally follow from the matrix integral representation.