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

Freedman, Daniel Z.; Pilch, Krzysztof; Pufu, Silviu S.; Warner, Nicholas P.

doi:10.1007/JHEP06(2017)053

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

Journal Article · Mon Jun 12 00:00:00 EDT 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP06(2017)053· OSTI ID:1426908

Freedman, Daniel Z. ^[1]; Pilch, Krzysztof ^[2]; Pufu, Silviu S. ^[3]; Warner, Nicholas P. ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Stanford Univ., CA (United States)
Univ. of Southern California, Los Angeles, CA (United States)
Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics

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 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 AdS₄ 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 OIJ. 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 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.

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Research Organization:: Univ. of Southern California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0011687

OSTI ID:: 1426908

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 6; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 29 works

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