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A universal formula for the $x-y$ swap in topological recursion

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arxiv 2212.00320 v3 pith:T54GPBJD submitted 2022-12-01 math-ph hep-thmath.AGmath.COmath.MP

classification math-phhep-thmath.AGmath.COmath.MP
keywords formularecursionswaptopologicaluniversalcloseddifferentialsprove
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abstract

We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock). As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$.

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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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