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Calculating the partition function of \( \mathcal{N} = 2 \) gauge theories on S 3 and AdS/CFT correspondence

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Abstract

We test the AdS/CFT correspondence by computing the partition function of some \( \mathcal{N} = 2 \) quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds Q 1,1,1 or V 5,2. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to N 3/2 and the coefficient matches correctly the volume of Q 1,1,1 and V 5,2.

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Authors and Affiliations

  1. Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul, 151-747, Korea

    Sangmo Cheon

  2. Department of Physics and Research Institute of Basic Science, Kyung Hee University, 1 Hoegi-dong, Dongdaemun-gu, Seoul, 130-701, Korea

    Hyojoong Kim & Nakwoo Kim

  3. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada

    Nakwoo Kim

Authors
  1. Sangmo Cheon
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  2. Hyojoong Kim
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  3. Nakwoo Kim
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Correspondence to Nakwoo Kim.

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ArXiv ePrint: 1102.5565

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Cheon, S., Kim, H. & Kim, N. Calculating the partition function of \( \mathcal{N} = 2 \) gauge theories on S 3 and AdS/CFT correspondence. J. High Energ. Phys. 2011, 134 (2011). https://doi.org/10.1007/JHEP05(2011)134

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