Generalized Mariño-Vafa Formula and Local Gromov-Witten Theory of Orbi-curves

Abstract

We prove a generalized Mariño-Vafa formula for Hodge integrals over $\Mbar_{g, γ-μ}(\cB G)$ with $G$ an arbitrary finite abelian group. Then we use this formula to study the local Gromov-Witten theory of an orbi-curve with cyclic stack points in a Calabi-Yau three-orbifold.