A universal formula for the $x-y$ swap in topological recursion
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 .
Authors
- Petr Dunin‐Barkowski (ORCID: https://orcid.org/0000-0003-1475-0534)
- Boris Sergeevich Bychkov (ORCID: https://orcid.org/0000-0002-4441-9343)
- A. Alexandrov (ORCID: https://orcid.org/0000-0002-8464-254X)
- Maxim Eduardovich Kazarian (ORCID: https://orcid.org/0000-0002-3928-8799)
- Sergey Viktorovich Shadrin (ORCID: https://orcid.org/0000-0002-4139-9754)
Institutions
- National Research University Higher School of Economics (RU)
- Skolkovo Institute of Science and Technology (RU)
- Institute for Basic Science (KR)
- Institute for Theoretical and Experimental Physics (RU)
- Amsterdam University of the Arts (NL)
- University of Amsterdam (NL)
- University of Haifa (IL)
Publication Details
- Journal
- Journal of the European Mathematical Society
- Published
- 2025-04-14
- DOI
- https://doi.org/10.4171/jems/1615
- Citations
- 6
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 22.15