On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit

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 ε_{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.

41 pages, no figure. v2: references added

References in corpus (7)

• The Refined Topological Vertex
• Holomorphic anomaly and matrix models
• Extended Holomorphic Anomaly in Gauge Theory
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Topological Strings and (Almost) Modular Forms

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