# Open intersection numbers, Kontsevich-Penner model and cut-and-join operators

@article{Alexandrov2014OpenIN,
title={Open intersection numbers, Kontsevich-Penner model and cut-and-join operators},
author={Alexander Alexandrov},
journal={Journal of High Energy Physics},
year={2014},
volume={2015},
pages={1-25}
}
• A. Alexandrov
• Published 11 December 2014
• Mathematics
• Journal of High Energy Physics
A bstractWe continue our investigation of the Kontsevich-Penner model, which describes intersection theory on moduli spaces both for open and closed curves. In particular, we show how Buryak’s residue formula, which connects two generating functions of intersection numbers, appears in the general context of matrix models and tau-functions. This allows us to prove that the Kontsevich-Penner matrix integral indeed describes open intersection numbers. For arbitrary N we show that the string and…
• Mathematics
• 2017
A bstractA 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
• Mathematics
Journal of High Energy Physics
• 2017
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
• Mathematics
Annales Henri Poincaré
• 2018
We identify the Kontsevich–Penner matrix integral, for finite size n, with the isomonodromic tau function of a $$3\times 3$$3×3 rational connection on the Riemann sphere with n Fuchsian singularities
We present a simplified formulation of open intersection numbers, as an alternative to the theory initiated by Pandharipande, Solomon and Tessler. The relevant moduli spaces consist of Riemann
• Mathematics
• 2015
The s-point correlation function of a Gaussian Hermitian random matrix model, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli
. In this paper, we consider the higher Br´ezin–Gross–Witten tau-functions, given by the matrix integrals. For these tau-functions we construct the canonical Kac–Schwarz operators, quantum spectral
Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of
The Brezin-Gross-Witten model is one of the basic examples in the class of non-eigenvalue unitary matrix models. In the Kontsevich phase, it is a tau-function for the KdV hierarchy. In this paper we

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