Topological open strings on orbifolds

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.

38 pages

References in corpus (11)

• Open string amplitudes and large order behavior in topological string theory
• Remodeling the B-model
• Free energy topological expansion for the 2-matrix model
• Direct Integration of the Topological String
• Holomorphic anomaly and matrix models
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
• Polynomial Structure of the (Open) Topological String Partition Function
• Topological Strings and (Almost) Modular Forms
• Large N gauge theories and topological cigars
• The holomorphic anomaly for open string moduli

Cited by in corpus (17)

• A & B model approaches to surface operators and Toda theories
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• The uses of the refined matrix model recursion
• Think globally, compute locally
• A generalized topological recursion for arbitrary ramification
• Crepant resolutions and open strings
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Topological string amplitudes for the local half K3 surface
• The remodeling conjecture and the Faber-Pandharipande formula
• Quantum curves from refined topological recursion: the genus 0 case
• Open Gromov-Witten Theory of $K_{{\mathbb{P}}^2},K_{{\mathbb{P}}^1\times {\mathbb{P}}^1},K_{W\mathbb{P}[1,1,2]},K_{{\mathbb{F}}_1}$ and Jacobi Forms
• Taming open/closed string duality with a Losev trick
• Flat Connections in Open String Mirror Symmetry
• Open/Closed BPS Correspondence and Integrality
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• Refined topological recursion revisited -- properties and conjectures