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Exact results on ABJ theory and the refined topological string

  • Masazumi HondaEmail author
  • Kazumi Okuyama
Open Access
Article

Abstract

We study the partition function of the ABJ theory, which is the \( \mathcal{N}=6 \) superconformal Chern-Simons matter theory with gauge group U(N) × U(N + M) and Chern-Simons levels (k, −k). We exactly compute the ABJ partition function on a three sphere for various k, M and N via the Fermi gas approach. By using these exact data, we show that the ABJ partition function is completely determined by the refined topological string on local \( {\mathbb{P}}^1\times {\mathbb{P}}^1 \), including membrane instanton effects in the M-theory dual.

Keywords

Matrix Models AdS-CFT Correspondence Topological Strings M-Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Harish-Chandra Research InstituteAllahabadIndia
  2. 2.Department of PhysicsShinshu UniversityMatsumotoJapan

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