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arXiv · 2405.10720

Symplectic duality via log topological recursion

Alexander Alexandrov·Boris Bychkov·Petr Dunin-Barkowski·Maxim Kazarian·Sergey Shadrin
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Abstract

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log topological recursion. As a corollary, we establish nice properties of symplectic duality: various convenient explicit formulas, invertibility, group property, compatibility with topological recursion and KP integrability. As an application of these properties, we get a new and uniform proof of topological recursion for large families of weighted double Hurwitz numbers; this encompasses and significantly extends all previously known results on this matter.

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Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin. 2024-05-17. Symplectic duality via log topological recursion. https://doi.org/10.4310/cntp.241203001416

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