mirror symmetry for orbifold hurwitz numbers

• DOI: 10.48550/arxiv.1301.4871
• Publication Date: 2014-09-01
• Authors: Bouchard, Vincent; Serrano, Daniel H...; Liu, Xiaojun; Mulase, Motohico
• Keywords: High Energy Physics - Theory; hep-th; General Mathematics; math-ph; FOS: Physical sciences; Mathematical Physics (math-ph); Pure Mathematics; 01 natural sciences; math.AG; Mathematics - Algebraic Geometry; math.MP; High Energy Physics - Theory (hep-th); FOS: Mathematics; 0101 mathematics; Algebraic Geometry (math.AG); Mathematical Physics

39 pages, 2 figures<br/>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.<br/>