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arXiv · 1301.4871

Mirror symmetry for orbifold Hurwitz numbers

Vincent Bouchard·Daniel Hernandez Serrano·Xiaojun Liu·Motohico Mulase
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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.

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Vincent Bouchard, Daniel Hernandez Serrano, Xiaojun Liu, Motohico Mulase. 2013-01-21. Mirror symmetry for orbifold Hurwitz numbers. https://arxiv.org/abs/1301.4871

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