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|Abstract:||N = 8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators O-IJ with Delta = 1 in the 3 5(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-IJ. So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetryto 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 Delta = 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.|
|Electronic Publication Date:||12-Jun-2017|
|Citation:||Freedman, Daniel Z, Pilch, Krzysztof, Pufu, Silviu S, Warner, Nicholas P. (2017). Boundary terms and three-point functions: an Ads/CFT puzzle resolved. JOURNAL OF HIGH ENERGY PHYSICS, 10.1007/JHEP06(2017)053|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||JOURNAL OF HIGH ENERGY PHYSICS|
|Version:||Final published version. This is an open access article.|
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