Topological Strings on Elliptic Fibrations

Understand

We study topological string theory on elliptically fibered Calabi-Yau threefolds using mirror symmetry.

• We compute higher genus topological string amplitudes and express these in terms of polynomials of functions constructed from the special geometry of the moduli space.
• The polynomials are fixed by the holomorphic anomaly equations supplemented by the expected behavior at the boundary in moduli space.
• We further expand the amplitudes in the base moduli of the elliptic fibration and find that the fiber moduli dependence is captured by a finer polynomial structure in terms of the modular forms of the modular group of the elliptic curve.