Topological open strings on orbifolds

We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest. We exemplify this procedure for the ℂ3/ℤ3 orbifold point of local ℙ2, where we present results for topological string amplitudes for genus zero and up to three holes, and for the one-holed torus. These amplitudes can be understood as generating functions for either open orbifold Gromov-Witten invariants of ℂ3/ℤ3, or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators. © Springer-Verlag 2010