Global Properties of Topological String Amplitudes and Orbifold Invariants

Abstract

We derive topological string amplitudes on local Calabi-Yau manifolds in terms of polynomials in finitely many generators of special functions. These objects are defined globally in the moduli space and lead to a description of mirror symmetry at any point in the moduli space. Holomorphic ambiguities of the anomaly equations are fixed by global information obtained from boundary conditions at few special divisors in the moduli space. As an illustration we compute higher genus orbifold Gromov-Witten invariants for C^3/Z_3 and C^3/Z_4.

34 pages, 3 figures

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Cited by in corpus (15)

• The Omega deformed B-model for rigid N=2 theories
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Multi-Instantons and Multi-Cuts
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Direct Integration and Non-Perturbative Effects in Matrix Models
• Lectures on Mirror Symmetry and Topological String Theory
• Special Polynomial Rings, Quasi Modular Forms and Duality of Topological Strings
• Differential Rings from Special Kähler Geometry
• Topological Strings on Elliptic Fibrations
• 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
• Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• Flat Connections in Open String Mirror Symmetry
• Local B-model and Mixed Hodge Structure
• Algebraic structure of $t{t}^{\ast }$ equations for Calabi-Yau sigma models