Journal article

Topological recursion on the Bessel curve

Norman Do, Paul Norbury

COMMUNICATIONS IN NUMBER THEORY AND PHYSICS | INT PRESS BOSTON, INC | Published : 2018

Abstract

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 si..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Counci


Funding Acknowledgements

The first author was supported by the Australian Research Council grant DE130100650. The authors would like to thank Alexander Alexandrov for numerous discussions, Maksim Karev for comments on an earlier version of the manuscript, and the referees for their insightful suggestions to improve the paper.