Boundary terms and threepoint functions: an AdS/CFT puzzle resolved
N=8 superconformal field theories, such as the ABJM theory at ChernSimons level k = 1 or 2, contain 35 scalar operators O _{IJ} with Δ = 1 in the 35 v representation of SO(8). The 3point correlation function of these operators is nonvanishing, and indeed can be calculated nonperturbatively 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 OIJ. 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 3point 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 onshell action, and the supersymmetry properties of this functional play a significant role in our treatment.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[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
 Publication Date:
 Grant/Contract Number:
 SC0011687
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of Southern California, Los Angeles, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
 OSTI Identifier:
 1426908
Freedman, Daniel Z., Pilch, Krzysztof, Pufu, Silviu S., and Warner, Nicholas P.. Boundary terms and threepoint functions: an AdS/CFT puzzle resolved. United States: N. p.,
Web. doi:10.1007/JHEP06(2017)053.
Freedman, Daniel Z., Pilch, Krzysztof, Pufu, Silviu S., & Warner, Nicholas P.. Boundary terms and threepoint functions: an AdS/CFT puzzle resolved. United States. doi:10.1007/JHEP06(2017)053.
Freedman, Daniel Z., Pilch, Krzysztof, Pufu, Silviu S., and Warner, Nicholas P.. 2017.
"Boundary terms and threepoint functions: an AdS/CFT puzzle resolved". United States.
doi:10.1007/JHEP06(2017)053. https://www.osti.gov/servlets/purl/1426908.
@article{osti_1426908,
title = {Boundary terms and threepoint functions: an AdS/CFT puzzle resolved},
author = {Freedman, Daniel Z. and Pilch, Krzysztof and Pufu, Silviu S. and Warner, Nicholas P.},
abstractNote = {N=8 superconformal field theories, such as the ABJM theory at ChernSimons level k = 1 or 2, contain 35 scalar operators OIJ with Δ = 1 in the 35 v representation of SO(8). The 3point correlation function of these operators is nonvanishing, and indeed can be calculated nonperturbatively 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 3point 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 onshell action, and the supersymmetry properties of this functional play a significant role in our treatment.},
doi = {10.1007/JHEP06(2017)053},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2017,
place = {United States},
year = {2017},
month = {6}
}