Mirror Symmetry for Orbifold Hurwitz Numbers
نویسندگان
چکیده
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.
منابع مشابه
Edge-contraction on Dual Ribbon Graphs, 2d Tqft, and the Mirror of Orbifold Hurwitz Numbers
We present a new set of axioms for a 2D TQFT formulated on the category of the dual of ribbon graphs with edge-contraction operations as morphisms. Every Frobenius algebra A determines a contravariant functor from this category to the category of elements of the tensor category of Frobenius algebras over A∗. The functor evaluated at connected graphs is the TQFT corresponding to A. The edge-cont...
متن کاملA Relative Riemann-hurwitz Theorem, the Hurwitz-hodge Bundle, and Orbifold Gromov-witten Theory
We provide a formula describing the G-module structure of the Hurwitz-Hodge bundle for admissible G-covers in terms of the Hodge bundle of the base curve, and more generally, for describing the G-module structure of the push-forward to the base of any sheaf on a family of admissible Gcovers. This formula can be interpreted as a representation-ring-valued relative Riemann-Hurwitz formula for fam...
متن کاملChiodo formulas for the r-th roots and topological recursion
We analyze Chiodo’s formulas for the Chern classes related to the r -th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with ψ-classes are reproduced via the Chekhov–Eynard–Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz nu...
متن کامل1 0 Se p 20 07 Hurwitz numbers , matrix models and enumerative geometry
We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi–Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topol...
متن کاملar X iv : 0 70 9 . 14 58 v 2 [ m at h . A G ] 8 J un 2 00 8 Hurwitz numbers , matrix models and enumerative geometry
We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi–Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topol...
متن کامل