Global Properties of Topological String Amplitudes and Orbifold Invariants

Understand

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.