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KP integrability through the $x-y$ swap relation

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arxiv 2309.12176 v3 pith:35N5XFY3 submitted 2023-09-21 math-ph hep-thmath.MPnlin.SI

Alexander Alexandrov , Boris Bychkov , Petr Dunin-Barkowski , Maxim Kazarian , Sergey Shadrin This is my paper
classification math-phhep-thmath.MPnlin.SI
keywords relationswaptheoryintegrabilityrecursiontopologicalapplicationcall
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universal Correlators on Exponentially Ramified Spectral Curves

    math-ph 2026-07 conditional novelty 6.0 of 10

    Generalized topological recursion extends to spectral curves with essential singularities by replacing residues at the essential point with residues at ordinary meromorphic points.

  2. $x-y$ swap for $(2,2p+1)$ minimal string

    hep-th 2025-06 conditional novelty 6.0 of 10

    An x-y swapped spectral curve is conjectured to reproduce (2,2p+1) minimal string tachyon correlators without resonance transformations; verified at low genus, with a ground-ring extension that does not match HEM.

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