A universal formula for the $x-y$ swap in topological recursion
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918034995675136 |
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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 prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock).
As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_00320 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A universal formula for the $x-y$ swap in topological recursion Alexandrov, Alexander Bychkov, Boris Dunin-Barkowski, Petr Kazarian, Maxim Shadrin, Sergey Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics We prove a recent conjecture of Borot et al. that a particular universal closed algebraic formula recovers the correlation differentials of topological recursion after the swap of $x$ and $y$ in the input data. We also show that this universal formula can be drastically simplified (as it was already done by Hock). As an application of this general $x-y$ swap result, we prove an explicit closed formula for the topological recursion differentials for the case of any spectral curve with unramified $y$ and arbitrary rational $x$. |
| title | A universal formula for the $x-y$ swap in topological recursion |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2212.00320 |