Open intersection numbers, matrix models and 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.

15 pages; minor corrections

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• Higher Airy structures, W algebras and topological recursion
• KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model
• The Kontsevich-Penner matrix integral, isomonodromic tau functions and open intersection numbers
• The Harer--Zagier recursion for an irregular spectral curve
• Genus expansion of open free energy in 2d topological gravity
• Matrix models for stationary Gromov-Witten invariants of the Riemann sphere
• From minimal gravity to open intersection theory
• On affine coordinates of the tau-function for open intersection numbers
• Integrable systems associated to open extensions of type A and D Dubrovin-Frobenius manifolds