On Three-point Functions in the AdS_4/CFT_3 Correspondence

Abstract

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

arXiv comment24 pages. v2: typos corrected, references added, published version

References in corpus (51)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Transcendentality and Crossing
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• Spin chains and string theory
• Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Aspects of Semiclassical Strings in AdS${}_5$
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• The Bethe ansatz for superconformal Chern-Simons
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The all loop AdS4/CFT3 Bethe ansatz
• Tailoring Three-Point Functions and Integrability
• From correlation functions to Wilson loops
• The super-correlator/super-amplitude duality: Part I
• On three-point correlation functions in the gauge/gravity duality
• Holographic three-point functions of semiclassical states
• On correlation functions of operators dual to classical spinning string states
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• More on the duality correlators/amplitudes
• Holographic three-point functions of giant gravitons
• On semiclassical approximation for correlators of closed string vertex operators in AdS/CFT
• Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
• A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
• Quantum Integrability for Three-Point Functions
• Classical Limit of the Three-Point Function from Integrability
• SL(2) sector: weak/strong coupling agreement of three-point correlators
• Extremal vs. Non-Extremal Correlators with Giant Gravitons
• Three Point Functions of Chiral Primary Operators in d=3, N= 8 and d=6, N=(2,0) SCFT at Large N
• Tailoring Three-Point Functions and Integrability IV. Theta-morphism
• From Correlators to Wilson Loops in Chern-Simons Matter Theories
• Giant gravitons and correlators
• A note on the eigenvectors of long-range spin chains and their scalar products
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Holographic 3-point function at one loop
• Giant Gravitons on AdS_4 x CP^3 and their Holographic Three-point Functions
• On correlation functions of Wilson loops, local and non-local operators
• Exact Large R-charge Correlators in ABJM Theory
• On semiclassical calculation of three-point functions in AdS_4 x CP^3
• On semiclassical calculation of three-point functions in AdS_5 \times T^(1,1)
• Matching three-point functions of BMN operators at weak and strong coupling
• Correlators of Giant Gravitons from dual ABJ(M) Theory
• Bosonic Quadratic Actions for 11D Supergravity on AdS_7/4 x S_4/7
• The SO(6) Scalar Product and Three-Point Functions from Integrability
• Three-point functions of BMN operators at weak and strong coupling II. One loop matching
• Slavnov determinants, Yang-Mills structure constants, and discrete KP
• OPE in planar QCD from integrability

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• Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved
• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
• Leading finite-size effects on some three-point correlators in AdS_5 x S^5
• Correlation functions of the ABJM model
• Three-Point Functions in ABJM and Bethe Ansatz
• Three-point Functions in Aharony--Bergman--Jafferis--Maldacena Theory and Integrable Boundary States
• Some semiclassical structure constants for AdS_4 x CP^3
• Three-point functions of semiclassical string states and conserved currents in AdS_4 x CP^3