Mirror symmetry for orbifold Hurwitz numbers

@article{Bouchard2013MirrorSF,
  title={Mirror symmetry for orbifold Hurwitz numbers},
  author={Vincent Bouchard and Daniel Hern{\'a}ndez Serrano and Xiaojun Liu and Motohico Mulase},
  journal={Journal of Differential Geometry},
  year={2013},
  volume={98},
  pages={375-423}
}
We study mirror symmetry for orbifold Hurwitz numbers. We show that the Laplace transform of orbifold Hurwitz numbers satisfy a dierential 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 innite framing limit of orbifold Gromov-Witten theory of (C 3 =(Z=rZ)). Finally, we prove that the mirror model to orbifold Hurwitz numbers admits a quantum… 
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