Large N Free Energy of 3d N = 4 SCFTs and AdS4/CFT3

A bstract We provide a non-trivial check of the AdS 4 /CFT 3 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 =4SCFT T [ SU ( N )]. ThisismatchedwiththecomputationofthetypeIIBactionon the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2N²ln N . We also extend our results to richer Tρρ ̂ [ SU ( N )] theories and argue that 1/2N²ln N ln N is the maximal free energy at large N in this class of gauge theories.