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<p>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 <i>r</i>-th roots of the twisted powers of the log canonical bundles.</p>

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Any Topological Recursion on a Rational Spectral Curve is KP Integrable

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月9日

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  • A. Alexandrov,
  • B. Bychkov,
  • P. Dunin-Barkowski,
  • M. Kazarian,
  • S. Shadrin

摘要

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.