Exact results for topological strings on resolved Y(p,q) singularities

Understand

We obtain exact results in \alpha' for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge theories.

• The toric Calabi-Yau's that we analyze are obtained as minimal resolution of cones over Y(p,q) manifolds and give rise via M-theory compactification to SU(p) gauge theories on R^4 x S^1.
• As an application we present a detailed study of the local F_2 case and compute open and closed genus zero Gromov-Witten invariants of the C^3/Z_4 orbifold.
• We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes.The mirror curve in this case is the spectral curve of the relativistic A_1 Toda chain.