Localization and gluing of orbifold amplitudes: The Gromov-Witten orbifold vertex

Abstract

We define a formalism for computing open orbifold GW invariants of $[\mathbb {C}^3/G]$, where $G$ is any finite abelian group. We prove that this formalism and a suitable gluing algorithm can be used to compute GW invariants in all genera of any toric CY orbifold of dimension $3$. We conjecture a correspondence with the DT orbifold vertex of Bryan-Cadman-Young.