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Any Topological Recursion on a Rational Spectral Curve is KP Integrable.

A Alexandrov1, B Bychkov2, P Dunin-Barkowski3,4,5

  • 1Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, 37673 Korea.

Communications in Mathematical Physics
|March 12, 2026
PubMed
Summary
This summary is machine-generated.

We demonstrate that correlation differentials from topological recursion are KP integrable for genus zero spectral curves. This confirms KP integrability for partition functions linked to log canonical bundles via ELSV-type formulas.

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Area of Science:

  • Mathematics
  • Mathematical Physics

Background:

  • Topological recursion is a powerful tool for studying discrete structures in quantum field theory and string theory.
  • KP integrability is a significant property in soliton theory and mathematical physics, indicating deep underlying structures.

Purpose of the Study:

  • To prove the KP integrability of correlation differentials in topological recursion for genus zero spectral curves.
  • To establish the KP integrability of partition functions associated with log canonical bundles using ELSV-type formulas.

Main Methods:

  • Utilizing properties of spectral curves and topological recursion.
  • Applying ELSV-type formulas to relate partition functions to correlation differentials.

Main Results:

  • We prove that correlation differentials of topological recursion are KP integrable for any initial data on a genus zero spectral curve.
  • We establish the KP integrability of partition functions associated with the r-th roots of twisted powers of log canonical bundles.

Conclusions:

  • The findings confirm a deep connection between topological recursion and KP integrability.
  • This work opens new avenues for exploring integrable structures in mathematical physics and related fields.