Boundary terms and three-point functions: an AdS/CFT puzzle resolved

• Main Authors: Pilch, Krzysztof (Author), Warner, Nicholas P. (Author), Freedman, Daniel Z (Contributor), Pufu, Silviu (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: Springer Nature, 2018-06-25T14:40:07Z.
• Subjects: Article
• Online Access: Get fulltext

 N= 8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O I J with Δ = 1 in the 35 v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS 4 gravity dual, obtained from gauged N= 8 supergravity, has no cubic A 3 couplings in its Lagrangian, where A IJ is the bulk dual of O I J . So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS 4 boundary requires the introduction of a finite A 3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.