Letters in Mathematical Physics

, Volume 104, Issue 1, pp 75–87 | Cite as

From Hurwitz Numbers to Kontsevich–Witten Tau-Function: A Connection by Virasoro Operators

  • Alexander Alexandrov


In this letter, we present our conjecture on the connection between the Kontsevich–Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the GL(∞) group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of gl(∞). If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich–Witten tau-function.

Mathematics Subject Classification (2010)

Primary 37K10 14N35 81R10 17B68 Secondary 81T30 


matrix models tau-functions Virasoro algebra Hurwitz numbers 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of FreiburgFreiburgGermany
  2. 2.ITEPMoscowRussia

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