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KP integrability through the $x-y$ swap relation
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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.
Forward citations
Cited by 3 Pith papers
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An explicit four-corner dictionary for (2,p) minimal Liouville gravity
For the Lee-Yang series of minimal Liouville gravity, the four Frobenius and spectral-curve descriptions agree at genus zero after one per-insertion factor, and the resonance map is a tree-level Kontsevich frame change.
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Universal Correlators on Exponentially Ramified Spectral Curves
Generalized topological recursion extends to spectral curves with essential singularities by replacing residues at the essential point with residues at ordinary meromorphic points.
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$x-y$ swap for $(2,2p+1)$ minimal string
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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