Refined open intersection numbers and the Kontsevich-Penner matrix model

Abstract

A study of the intersection theory on the moduli space of Riemann surfaces with boundary was recently initiated in a work of R. Pandharipande, J. P. Solomon and the third author, where they introduced open intersection numbers in genus 0. Their construction was later generalized to all genera by J. P. Solomon and the third author. In this paper we consider a refinement of the open intersection numbers by distinguishing contributions from surfaces with different numbers of boundary components, and we calculate all these numbers. We then construct a matrix model for the generating series of the refined open intersection numbers and conjecture that it is equivalent to the Kontsevich-Penner matrix model. An evidence for the conjecture is presented. Another refinement of the open intersection numbers, which describes the distribution of the boundary marked points on the boundary components, is also discussed.

35 pages, 13 figures; references added

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• Matrix Models for Random Partitions
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Cited by in corpus (11)

• Developments in Topological Gravity
• The combinatorial formula for open gravitational descendents
• Higher Airy structures and topological recursion for singular spectral curves
• Quantization of Harer-Zagier formulas
• Open intersection numbers and free fields
• The Kontsevich-Penner matrix integral, isomonodromic tau functions and open intersection numbers
• Spectral Form Factor for Time-dependent Matrix model
• Matrix models for stationary Gromov-Witten invariants of the Riemann sphere
• From minimal gravity to open intersection theory
• d-orthogonal polynomials, Toda Lattice and Virasoro symmetries
• On affine coordinates of the tau-function for open intersection numbers