[Intégrabilité KP des différentielles non perturbatives]
We prove the KP integrability of non-perturbative topological recursion, which can be considered as a formal $\hbar $-deformation of the Krichever construction of algebro-geometric solutions of the KP hierarchy. This property goes back to a 2011 conjecture of Borot and Eynard.
Nous démontrons l’intégrabilité KP de la récursion topologique non perturbative, qui peut être vue comme une $\hbar $-déformation formelle de la construction de Krichever des solutions algébro-géométriques de la hiérarchie KP. Cette propriété remonte à une conjecture de Borot et Eynard datant de 2011.
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Keywords: Topological recursion, non-perturbative expansions, Krichever differentials, algebro-geometric solutions, KP hierarchy
Mots-clés : Récursion topologique, développements non perturbatifs, différentielles de Krichever, solutions algébro-géométriques, hiérarchie KP
Alexander Alexandrov 1 ; Boris Bychkov 2 ; Petr Dunin-Barkowski 3 ; Maxim Kazarian 4 ; Sergey Shadrin 5
CC-BY 4.0
Alexander Alexandrov; Boris Bychkov; Petr Dunin-Barkowski; Maxim Kazarian; Sergey Shadrin. KP integrability of non-perturbative differentials. Journal de l’École polytechnique — Mathématiques, Tome 13 (2026), pp. 1607-1635. doi: 10.5802/jep.356
@article{JEP_2026__13__1607_0,
author = {Alexander Alexandrov and Boris Bychkov and Petr Dunin-Barkowski and Maxim Kazarian and Sergey Shadrin},
title = {KP integrability of non-perturbative~differentials},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1607--1635},
year = {2026},
publisher = {\'Ecole polytechnique},
volume = {13},
doi = {10.5802/jep.356},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.356/}
}
TY - JOUR AU - Alexander Alexandrov AU - Boris Bychkov AU - Petr Dunin-Barkowski AU - Maxim Kazarian AU - Sergey Shadrin TI - KP integrability of non-perturbative differentials JO - Journal de l’École polytechnique — Mathématiques PY - 2026 SP - 1607 EP - 1635 VL - 13 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.356/ DO - 10.5802/jep.356 LA - en ID - JEP_2026__13__1607_0 ER -
%0 Journal Article %A Alexander Alexandrov %A Boris Bychkov %A Petr Dunin-Barkowski %A Maxim Kazarian %A Sergey Shadrin %T KP integrability of non-perturbative differentials %J Journal de l’École polytechnique — Mathématiques %D 2026 %P 1607-1635 %V 13 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.356/ %R 10.5802/jep.356 %G en %F JEP_2026__13__1607_0
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