KP integrability through the $x-y$ swap relation
Mathematical Physics
2025-05-13 v3 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
We discuss a universal relation that we call the 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 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.
Cite
@article{arxiv.2309.12176,
title = {KP integrability through the $x-y$ swap relation},
author = {Alexander Alexandrov and Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Shadrin},
journal= {arXiv preprint arXiv:2309.12176},
year = {2025}
}
Comments
28 pages; minor corrections