Projects per year
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 simple branch points.
Original language | English |
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Pages (from-to) | 53-73 |
Number of pages | 21 |
Journal | Communications in Number Theory and Physics |
Volume | 12 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Projects
- 1 Finished
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The geometry and combinatorics of moluli spaces
Do, N. (Primary Chief Investigator (PCI))
ARC - Australian Research Council
30/06/13 → 30/08/18
Project: Research