Symplectic duality via log topological recursion
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910727340556288 |
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| author | Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey |
| author_facet | Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10720 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symplectic duality via log topological recursion Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics 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. |
| title | Symplectic duality via log topological recursion |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2405.10720 |