Work

A universal formula for the $x-y$ swap in topological recursion

Year: 2025

Type: article

Abstract: 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 .

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1615

Authors: Alexander Alexandrov, Boris Bychkov, Petr Dunin-Barkowski, Maxim Kazarian, Sergey Shadrin

Institutions: Institute for Basic Science, University of Haifa, National Research University Higher School of Economics, Skolkovo Institute of Science and Technology, Institute for Theoretical and Experimental Physics, University of Amsterdam

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4409430481

FWCI: 12.71

Cites:

Cited by: 11

Related to: 10