## Abstract

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.

Original language | English (US) |
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Article number | 53 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2017 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

## Keywords

- AdS-CFT Correspondence
- Extended Supersymmetry
- Supergravity Models