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Mosc. Math. J., 2016, Volume 16, Number 1, Pages 27–44 (Mi mmj593)  

This article is cited in 7 scientific papers (total in 7 papers)

Open intersection numbers and the wave function of the KdV hierarchy

A. Buryak

Department of Mathematics, ETH Zurich, Ramistrasse 101 8092, HG G 27.1, Zurich, Switzerland

Abstract: 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 intersection numbers is a specific solution of a system of PDEs, which they called the open KdV equations. In this paper we show that the open KdV equations are closely related to the equations for the wave function of the KdV hierarchy. This allows us to give an explicit formula for the specific solution in terms of Witten's generating series of the intersection numbers on the moduli space of stable curves.

Key words and phrases: Riemann surfaces with boundary, moduli space, KdV equations.

Funding Agency Grant Number
Eidgenösische Technische Hochschule Zürich ERC-2012-AdG-320368-MCSK
Ministry of Education and Science of the Russian Federation 11.634.31.0005
NSh-4850.2012.1
Russian Foundation for Basic Research 13-01-00755
This work was supported by grant ERC-2012-AdG-320368-MCSK in the group of R. Pandharipande at ETH Zurich, by the Russian Federation Government grant no. 2010-220-01-077 (ag. no. 11.634.31.0005), the grants RFFI 13-01-00755 and NSh-4850.2012.1.


DOI: https://doi.org/10.17323/1609-4514-2016-16-1-27-44

Full text: http://www.mathjournals.org/.../2016-016-001-002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 35Q53; Secondary 14H10
Received: October 16, 2014; in revised form April 23, 2015
Language:

Citation: A. Buryak, “Open intersection numbers and the wave function of the KdV hierarchy”, Mosc. Math. J., 16:1 (2016), 27–44

Citation in format AMSBIB
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\by A.~Buryak
\paper Open intersection numbers and the wave function of the KdV hierarchy
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 1
\pages 27--44
\mathnet{http://mi.mathnet.ru/mmj593}
\crossref{https://doi.org/10.17323/1609-4514-2016-16-1-27-44}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3470575}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386360200002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Buryak A., Janda F., Pandharipande R., “the Hypergeometric Functions of the Faber-Zagier and Pixton Relations”, Pure Appl. Math. Q., 11:4, 1, SI (2015), 591–631  crossref  mathscinet  zmath  isi
    2. A. Alexandrov, A. Buryak, R. J. Tessler, “Refined open intersection numbers and the Kontsevich–Penner matrix model”, J. High Energy Phys., 2017, no. 3, 123  crossref  mathscinet  isi  scopus
    3. K. Aleshkin, V. Belavin, Ch. Rim, “Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk”, J. High Energy Phys., 2017, no. 11, 169  crossref  mathscinet  zmath  isi  scopus
    4. A. Alexandrov, “Open intersection numbers and free fields”, Nucl. Phys. B, 922 (2017), 247–263  crossref  mathscinet  zmath  isi  scopus
    5. A. Buryak, R. J. Tessler, “Matrix models and a proof of the open analog of Witten's conjecture”, Commun. Math. Phys., 353:3 (2017), 1299–1328  crossref  mathscinet  zmath  isi  scopus
    6. A. Bawane, H. Muraki, Ch. Rim, “Open KdV hierarchy and minimal gravity on disk”, Phys. Lett. B, 783 (2018), 183–185  crossref  mathscinet  zmath  isi  scopus
    7. L. Chekhov, M. Mazzocco, “Colliding holes in Riemann surfaces and quantum cluster algebras”, Nonlinearity, 31:1 (2018), 54–107  crossref  mathscinet  zmath  isi  scopus
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