Large N Free Energy of 3d N=4 SCFTs and AdS/CFT

TL;DR

This paper verifies the AdS_4/CFT_3 correspondence for 3d N=4 SCFTs by matching free energy calculations from field theory and gravity at large N, revealing a leading behavior of 1/2 N^2 ln N.

Contribution

It provides the first non-trivial check of the AdS_4/CFT_3 duality for N=4 theories using free energy computations and extends the analysis to more complex theories.

Findings

Large N free energy scales as 1/2 N^2 ln N.

Matching of field theory and gravity calculations confirms the duality.

1/2 N^2 ln N is the maximal free energy in this class of theories.

Abstract

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.