## Integrable differential systems of topological type and reconstruction by the topological recursion

- Raphaël Belliard, Bertrand Eynard, Olivier Marchal
- 2016

2 Excerpts

- Published 2016

The Witten–Kontsevich theorem states that a certain generating function for intersection numbers on the moduli space of stable curves is a tau-function for the KdV integrable hierarchy. This generating function can be recovered via the topological recursion applied to the Airy curve x = 1 2 y 2. In this paper, we consider the topological recursion applied to the irregular spectral curve xy2 = 2 , which we call the Bessel curve. We prove that the associated partition function is also a KdV tau-function, which satisfies Virasoro constraints, a cut-and-join type recursion, and a quantum curve equation. Together, the Airy and Bessel curves govern the local behaviour of all spectral curves with simple branch points.

@inproceedings{Do2016TopologicalRO,
title={Topological recursion on the Bessel curve},
author={Norman Do and Paul T. Norbury},
year={2016}
}