On gauge theory and topological string in Nekrasov-Shatashvili limit

• Published in: The journal of high energy physics Vol. 2012; no. 6
• Main Author: Huang, Min-xin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2012; Springer Nature B.V
• Subjects: Amplitudes; Boundary conditions; Classical and Quantum Gravitation; Differential equations; Differential geometry; Elementary Particles; Gauge theory; High energy physics; Mathematical analysis; Parameters; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Topology; Topological Strings; Supersymmetric gauge theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2012)152

We study the Nekrasov-Shatashvili limit of the
= 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 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.