N= 8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators OI J with Δ = 1 in the 35v 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 AdS4 gravity dual, obtained from gauged N= 8 supergravity, has no cubic A3 couplings in its Lagrangian, where AIJ is the bulk dual of OI J. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS4 boundary requires the introduction of a finite A3 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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- AdS-CFT Correspondence
- Extended Supersymmetry
- Supergravity Models