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

We provide a non-trivial check of the AdS(4)/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 = 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 T-rho((rho) over cap)[SU(N)] theories and argue that 1/2 N-2 ln N is the maximal free energy at large N in this class of gauge theories.