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Journal of High Energy Physics

, 2013:46 | Cite as

Direct derivation of “mirror” ABJ partition function

  • Masazumi HondaEmail author
Article

Abstract

We study the partition function of the three-dimensional \( \mathcal{N} \) = 6 U(N) k × U(N + M)k superconformal Chern-Simons matter theory known as the ABJ theory. We prove that the ABJ partition function on S 3 is exactly the same as a formula recently proposed by Awata, Hirano and Shigemori. While this formula was previously obtained by an analytic continuation from the L(2, 1) lens space matrix model, we directly derive this by using a generalization of the Cauchy determinant identity. We also give an interpretation for the formula from brane picture.

Keywords

Matrix Models Supersymmetry and Duality M-Theory 

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Copyright information

© The Author(s) 2013

Authors and Affiliations

  1. 1.High Energy Accelerator Research Organization (KEK)TsukubaJapan
  2. 2.Yukawa Institute for Theoretical PhysicsKyoto UniversitySakyo-kuJapan

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