Boundary terms and three-point functions: an AdS/CFT puzzle resolved
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Freedman2017_Article_BoundaryTermsAndThree-pointFun.pdf
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Author(s)
Pilch, Krzysztof
Warner, Nicholas P.
Freedman, Daniel Z
Pufu, Silviu
Date Issued
June 2017
Journal
Journal of High Energy Physics
Publisher
Springer Nature
Citation
Freedman, Daniel Z., Krzysztof Pilch, Silviu S. Pufu, and Nicholas P. Warner. “Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved.” Journal of High Energy Physics 2017, no. 6 (June 2017).
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP06(2017)053
