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arXiv · 1205.3652

On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit

Min-xin Huang
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Abstract

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. We also provide a derivation of the holomorphic anomaly equations in the Nekrasov-Shatashvili limit from these differential equations.

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Min-xin Huang. 2012-05-16. On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit. https://doi.org/10.1007/jhep06(2012)152

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