Tuesday, January 22, 2013

1301.4871 (Vincent Bouchard et al.)

Mirror symmetry for orbifold Hurwitz numbers    [PDF]

Vincent Bouchard, Daniel Hernandez Serrano, Xiaojun Liu, Motohico Mulase
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.
View original: http://arxiv.org/abs/1301.4871

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