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Mirror symmetry for orbifold Hurwitz numbers

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.

preprint2013arXivOpen access
Vincent BouchardDaniel Hernandez SerranoXiaojun LiuMotohico Mulase
math-phmath.MPmath.AGhep-th
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Vincent BouchardDaniel Hernandez SerranoXiaojun LiuMotohico Mulase

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