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Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
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Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
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We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works (arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for 3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the type IIB action on the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We also extend our results to richer theories and argue that 1/2 N^2 ln N is the maximal free energy at large N in this class of gauge theories.
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Cited by 1 Pith paper
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Type IIB Supergravity Action and Holography
A milder topological correction to the PST Type IIB action yields non-vanishing on-shell values matching holography for Lunin-Maldacena and AdS4 S-fold backgrounds.
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