Research demonstrates KP integrability of topological recursion outcomes in rational spectral curves, suggesting broader implications in mathematical physics.
We prove that for any initial data on a genus zero spectral curve the corresponding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r -th roots of the twisted powers of the log canonical bundles.
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Alexandrov et al. (2026) studied this question.
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