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arXiv · 2309.12176

KP integrability through the $x-y$ swap relation

Alexander Alexandrov·Boris Bychkov·Petr Dunin-Barkowski·Maxim Kazarian·Sergey Shadrin
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Abstract

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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Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin. 2023-09-21. KP integrability through the $x-y$ swap relation. https://doi.org/10.1007/s00029-025-01035-8

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