Topological recursion on the Bessel curve

Norman Do, Paul Norbury

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


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 = 1/2y2. In this paper, we consider the topological recursion applied to the irregular spectral curve xy2 = 1/2, 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.

Original languageEnglish
Pages (from-to)53-73
Number of pages21
JournalCommunications in Number Theory and Physics
Issue number1
Publication statusPublished - 1 Jan 2018

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