On gauge theory and topological string in Nekrasov-Shatashvili limit

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• 作者：Min-xin Huang (1)
  
• 关键词：Supersymmetric gauge theory ; Topological Strings
• 刊名：Journal of High Energy Physics
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：2012
• 期：6
• 全文大小：603KB
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• 作者单位：Min-xin Huang (1)
  
  1. Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, Kashiwa, Chiba, 277-8582, Japan
  
• ISSN：1029-8479

文摘

We study the Nekrasov-Shatashvili limit of the $ \mathcal{N} $ =鈥? supersymmetric gauge theory and topological string theory on certain local toric Calabi-Yau manifolds. In this limit one of the two deformation parameters 系1,2 of the 惟 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.