Open intersection numbers, matrix models and MKP hierarchy

A. Alexandrov

Published 2014-10-07Version 1

In this paper we claim that the generating function of the intersection numbers on the moduli space 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 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.