Communications in Number Theory and Physics

Volume 9 (2015)

Number 4

The Eynard–Orantin recursion for simple singularities

Pages: 707 – 739



Todor Milanov (Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba, Japan)


According to [9] and [22], the ancestor correlators of any semisimple cohomological field theory satisfy local Eynard–Orantin recursion. In this paper, we prove that for simple singularities, the local recursion can be extended to a global one. The spectral curve of the global recursion is an interesting family of Riemann surfaces defined by the invariant polynomials of the corresponding Weyl group. We also prove that for genus $0$ and $1$, the free energies introduced in [10] coincide up to some constant factors with respectively the genus $0$ and $1$ primary potentials of the simple singularity.

Published 13 May 2016