Abstract
We provide a non-trivial check of the AdS4/CFT3 correspondence recently proposed in [1] by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works [2, 3] on the S 3 partition function for 3-dimensional N =4SCFTT[SU(N)]. ThisismatchedwiththecomputationofthetypeIIBactionon the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is \( \frac{1}{2}{N^2}\ln N \). We also extend our results to richer \( T_{\rho}^{\hat{\rho }} \) [SU (N )] theories and argue that \( \frac{1}{2}{N^2}\ln N \) ln N is the maximal free energy at large N in this class of gauge theories.
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ArXiv ePrint: 1206.2920
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Assel, B., Estes, J. & Yamazaki, M. Large N Free Energy of 3d \( \mathcal{N} \) = 4 SCFTs and AdS4/CFT3 . J. High Energ. Phys. 2012, 74 (2012). https://doi.org/10.1007/JHEP09(2012)074
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DOI: https://doi.org/10.1007/JHEP09(2012)074