On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit

Understand

We study the Nekrasov-Shatashvili limit of the N=2 supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau manifolds.

• In this limit one of the two deformation parameters \epsilon_{1,2} of the Omega background is set to zero and we study the perturbative expansion of the topological amplitudes around the remaining parameter.
• We derive differential equations from Seiberg-Witten curves and mirror geometries, which determine the higher genus topological amplitudes up to a constant.
• We show that the higher genus formulae previously obtained from holomorphic anomaly equations and boundary conditions satisfy these differential equations.