Mirror symmetry for orbifold Hurwitz numbers
Algebraic Geometry
2014-08-13 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a differential recursion, which is then proved to be equivalent to the integral recursion of Eynard and Orantin with spectral curve given by the r-Lambert curve. We argue that the r-Lambert curve also arises in the infinite framing limit of orbifold Gromov-Witten theory of [C3/(Z/rZ)]. Finally, we prove that the mirror model to orbifold Hurwitz numbers admits a quantum curve.
Keywords
Cite
@article{arxiv.1301.4871,
title = {Mirror symmetry for orbifold Hurwitz numbers},
author = {Vincent Bouchard and Daniel Hernandez Serrano and Xiaojun Liu and Motohico Mulase},
journal= {arXiv preprint arXiv:1301.4871},
year = {2014}
}
Comments
39 pages, 2 figures