Global Properties of Topological String Amplitudes and Orbifold Invariants

TL;DR

This paper develops a global framework for topological string amplitudes on local Calabi-Yau manifolds, enabling mirror symmetry analysis across the entire moduli space and computing orbifold Gromov-Witten invariants.

Contribution

It introduces a method to express topological string amplitudes as polynomials in special functions, fixing ambiguities via boundary conditions, and computes higher genus orbifold invariants.

Findings

Derived global topological string amplitudes in terms of special functions.

Fixed holomorphic ambiguities using boundary conditions at divisors.

Computed higher genus orbifold Gromov-Witten invariants for specific orbifolds.

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.