Abstract
We study the Nekrasov-Shatashvili limit of the \( \mathcal{N} \) = 2 supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau manifolds. In this limit one of the two deformation parameters ϵ1,2 of the Ω 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. We also provide a derivation of the holomorphic anomaly equations in the Nekrasov-Shatashvili limit from these differential equations.
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ArXiv ePrint: 1205.3652
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Huang, Mx. On gauge theory and topological string in Nekrasov-Shatashvili limit. J. High Energ. Phys. 2012, 152 (2012). https://doi.org/10.1007/JHEP06(2012)152
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DOI: https://doi.org/10.1007/JHEP06(2012)152