skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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 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 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 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.

Authors:
 [1];  [2];  [3];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Stanford Univ., CA (United States)
  2. Univ. of Southern California, Los Angeles, CA (United States)
  3. Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
Publication Date:
Research Org.:
Univ. of Southern California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1426908
Grant/Contract Number:
SC0011687
Resource Type:
Journal Article: 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 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Freedman, Daniel Z., Pilch, Krzysztof, Pufu, Silviu S., and Warner, Nicholas P. Boundary terms and three-point functions: an AdS/CFT puzzle resolved. United States: N. p., 2017. Web. doi:10.1007/JHEP06(2017)053.
Freedman, Daniel Z., Pilch, Krzysztof, Pufu, Silviu S., & Warner, Nicholas P. Boundary terms and three-point 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. Mon . "Boundary terms and three-point 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 three-point 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 Chern-Simons level k = 1 or 2, contain 35 scalar operators OIJ 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.},
doi = {10.1007/JHEP06(2017)053},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2017,
place = {United States},
year = {Mon Jun 12 00:00:00 EDT 2017},
month = {Mon Jun 12 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:
  • Recently, exact agreement has been found between bulk and boundary three-point functions in AdS{sub 3}xS{sup 3}xT{sup 4} with Neveu-Schwarz-Neveu-Schwarz (NSNS) fluxes. This represents a nontrivial check of AdS/CFT correspondence beyond the supergravity approximation as it corresponds to an exact worldsheet computation. When taking a closer look at this computation, one notices that a crucial point for the bulk-boundary agreement to hold is an intriguing mutual cancellation between worldsheet contributions corresponding to the AdS{sub 3} and to the S{sup 3} pieces of the geometry, that results in a simple factorized form for the final three-point function. In this note we reviewmore » this cancellation and clarify some points about the analytic relation between the SU(2) and the SL(2,R) structure constants. In particular, we dicuss the connection to the Coulomb gas representation. We also make some comments on the four-point function.« less
  • All cubic couplings in type IIB supergravity on AdS{sub 5}xS{sup 5} that involve two scalar fields s{sup I} that are mixtures of the five form field strength on S{sup 5} and the trace of the graviton on S{sup 5} are derived by using the covariant equations of motion and the quadratic action for type IIB supergravity on AdS{sub 5}xS{sup 5}. All corresponding three-point functions in SYM{sub 4} are calculated in the supergravity approximation. It is pointed out that the scalars s{sup I} correspond not to the chiral primary operators in the N=4 SYM but rather to a proper extension ofmore » the operators. (c) 2000 The American Physical Society.« less
  • We consider the leading large string tension correction to correlation functions of three vertex operators of particular massive string states in AdS{sub 5}xS{sup 5} string theory. We assume that two of these states are 'heavy' carrying large spins (of order string tension) and thus can be treated semiclassically while the third state is 'light' having fixed quantum numbers. We study several examples. In the case when the 'heavy' states are described by a folded string with large-spin in AdS{sub 5} the 3-point function scales as a semiclassical spin parameter of the 'heavy' state in power of the string level ofmore » the 'light' massive string state. We observe similar behavior in the case of 'heavy' states which admit a small angular momentum limit, which may thus represent creatures of three quantum massive string states.« less
  • Recently there has been progress on the computation of two- and three-point correlation functions with two heavy states via semiclassical methods. We extend this analysis to the case of AdS{sub 4}xCP{sup 3}, and examine the suggested procedure for the case of several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual N=6 Chern-Simons gauge theory.