TY - JOUR

T1 - Topological recursion on the Bessel curve

AU - Do, Norman

AU - Norbury, Paul

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85046089998&partnerID=8YFLogxK

U2 - 10.4310/CNTP.2018.v12.n1.a2

DO - 10.4310/CNTP.2018.v12.n1.a2

M3 - Article

AN - SCOPUS:85046089998

VL - 12

SP - 53

EP - 73

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

SN - 1931-4523

IS - 1

ER -