KP integrability through the swap relation

• A. Alexandrov ^[4] ; B. Bychkov ^[1] ; P. Dunin-Barkowski ^[2] ; M. Kazarian ^[2] ; S. Shadrin ^[3]
  1. [1] University of Haifa

     University of Haifa

     Israel

     
  2. [2] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  3. [3] University of Amsterdam

     University of Amsterdam

     Países Bajos

     
  4. [4] Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, Korea

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
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• Resumen

  • We discuss a universal relation that we call the x − y swap relation, which plays a prominent role in the theory of topological recursion, Hurwitz theory, and free probability theory. We describe in a very precise and detailed way the interaction of the x −y swap relation and KP integrability. As an application, we prove a recent conjecture that relates some particular instances of topological recursion to the Mironov–Morozov– Semenoff matrix integrals.

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