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KP integrability through the $$x-y$$ swap relation

Year: 2025
Type: article
Abstract: We discuss a universal relation that we call the $$x-y$$ 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 $$x-y$$ 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.
DOI: 10.1007/s00029-025-01035-8
Institutions: Institute for Basic Science, University of Haifa, National Research University Higher School of Economics, Skolkovo Institute of Science and Technology, Kurchatov Institute, University of Amsterdam
Language: English
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4409185083
FWCI: 5.848
Cites: 26
Cited by: 9
Related to: 10