Topological open strings on orbifolds

TL;DR

This paper applies the remodeling approach to the B-model topological string to analyze open string amplitudes on orbifolds, clarifying their modular properties and computing explicit amplitudes for the C^3/Z_3 orbifold.

Contribution

It introduces a method to study open string amplitudes on orbifolds using recursion relations and clarifies their modular transformation properties.

Findings

Computed genus zero and up to three-hole amplitudes for C^3/Z_3 orbifold

Revealed modular transformation properties of open amplitudes

Connected amplitudes to orbifold Gromov-Witten invariants and orbifold CFT correlators

Abstract

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 C^3/Z_3 orbifold point of local P^2, 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 C^3/Z_3, or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators.