Correlation functions in the CFT(d)/AdS(d+1) correpondence

Abstract

Conformal techniques are applied to the calculation of integrals on AdS(d+1) space which define correlators of composite operators in the superconformal field theory on the d-dimensional boundary. The 3-point amplitudes for scalar fields of arbitrary mass and gauge fields in the AdS supergravity are calculated explicitly. For 3 gauge fields we compare in detail with the known conformal structure of the SU(4) flavor current correlator <J_i^a J_j^b J_k^c> of the N=4, d=4 SU(N) SYM theory. Results agree with the free field approximation as would be expected from superconformal non-renormalization theorems. In studying the Ward identity relating <J_i^a O^I O^J> to <O^I O^J> for (non-marginal) scalar composite operators O^I, we find that there is a subtlety in obtaining the normalization of <O^I O^J> from the supergravity action integral.

27 pages, LaTex, 1 eps figure, few misprints corrected, references added

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• Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking
• Exploring Confinement in Anti-de Sitter Space
• DIS off glueballs from string theory: the role of the chiral anomaly and the Chern-Simons term
• Antipodally symmetric gauge fields and higher-spin gravity in de Sitter space
• Matching three-point functions of BMN operators at weak and strong coupling
• Massless BTZ black holes in minisuperspace
• On the M5 and the AdS7/CFT6 Correspondence
• Counterterms for the Dirichlet Prescription of the AdS/CFT Correspondence
• The Virtual Photon Structure Functions and AdS/QCD Correspondence
• Holographic phase transition and Quasinormal modes in Lovelock gravity
• Schwarzian correction to quantum correlation in SYK model
• Dual Geometry of Entanglement Entropy via Deep Learning
• Aspects of N-partite information in conformal field theories
• Revisiting Extremal Couplings in AdS/CFT
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Superconformal Ward Identities for Green Functions with Multiple Supercurrent Insertions
• Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Renormalization group in quantum critical theories with Harris-marginal disorder
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Metamorphosis of the Cosmological Constant and 5D Origin of the Fiducial Metric
• Vector Bosons in the Randall-Sundrum 2 and Lykken-Randall models and unparticles
• A CFT Distance Conjecture
• Scalar field spacetimes and the AdS/CFT conjecture
• Horizon complementarity in elliptic de Sitter space
• Near-Extremal Limits of Warped Black Holes
• Soft interaction at high energy and N=4 SYM
• AdS Box Graphs, Unitarity and Operator Product Expansions
• Quadratic corrections to three-point functions
• Quantum Information Metric on $\mathbb{R}\times S^{d-1}$
• 4-point correlators in finite-temperature AdS/CFT: jet quenching correlations
• Extremal Correlator of Three Vertex Operators for Circular Winding Strings in AdS5xS5
• Correlators of massive string states with conserved currents
• On universality of charge transport in AdS/CFT
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Semiclassical OPE coefficients from 3D gravity
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Gauged Supergravities from Spherical Reductions
• Second order equilibrium transport in strongly coupled $\mathcal{N}=4$ supersymmetric $SU(N_c)$ Yang-Mills plasma via holography
• $Ad{S}_5\times S^5$ supergravity vertex operators
• A note on R-currents and trace anomalies in the (2,0) tensor multiplet in d=6 and AdS/CFT correspondence
• Light-state Dominance from the Conformal Bootstrap
• Bulk Locality and Asymptotic Causal Diamonds
• Three-point functions at strong coupling in the BMN limit
• Sum rules and three point functions
• Remarks on Resonant Scalars in the AdS/CFT Correspondence
• Compact AdS space, Brane geometry and the AdS/CFT correspondence
• On some 3-point functions in the $W_4$ CFT and related braiding matrix
• Holographic four-point functions in Toda field theories in $Ad{S}_2$
• Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry
• Structure of the Electric Flux in N=4 Supersymmetric Yang-Mills Theory
• Finiteness of N =4 super-Yang-Mills effective action in terms of dressed N =1 superfields
• Semiclassical $p$-branes in hyperbolic space
• D-instantons and multiparticle production in N=4 SYM
• Long, partial-short, and special conformal fields
• Irrelevant Operators and their Holographic Anomalies
• Liouville theory and logarithmic solutions to Knizhnik-Zamolodchikov equation
• General graviton exchange graph for four point functions in the AdS/CFT correspondence
• Aspects of Holography in Conical $Ad{S}_3$
• On Holographic Weyl Anomaly
• Super Yang-Mills Operators from the D3-brane Action in a Curved Background
• Effective AdS/renormalized CFT
• Supersymmetric Black Holes and the SJT/nSCFT${}_1$ Correspondence
• Harmonic Analysis and Superconformal Gauge Theories in Three Dimensions from AdS/CFT Correspondence
• Towards S matrices on flat space and pp waves from SYM
• Bounds on Triangle Anomalies in (3+1)d
• The momentum analyticity of two-point correlators from perturbation theory and AdS/CFT
• Simplicity of AdS Supergravity at One Loop
• Propagators for p-forms in AdS_{2p+1} and correlation functions in the AdS_7/(2,0) CFT correspondence
• Examining Instabilities Due to Driven Scalars in AdS
• Holographic signatures of resolved cosmological singularities
• Brane running and AdS/CFT
• Jet evolution from weak to strong coupling
• AdS Duals of Matrix Strings
• Anomaly Inflow and Holography
• Holographic R-symmetric flows and the τ_U conjecture
• Thermalization of Holographic Excited States
• Aspects of dS/CFT Holography
• The Wess-Zumino Model and the AdS_4/CFT_3 Correspondence
• Explicitly Broken Supersymmetry with Exactly Massless Moduli
• A Solvable Sector of AdS Theory
• R-current six-point correlators in AdS_5 Supergravity
• RG flow of transport quantities
• Scalar Three-point Functions in a CDL Background
• Vector Fields in Kerr/CFT Correspondence
• BRST-BV approach to massless fields adapted to AdS/CFT correspondence
• Holography and quantum states in elliptic de Sitter space
• Chiral Magnetic Effect and Three-point Function from AdS/CFT Correspondence
• Late-time correlation functions in dS${}_3$/CFT${}_2$ correspondence
• Unimodular gravity and the gauge/gravity duality
• Four-point correlators in N=4 SYM from AdS${}_5$ bubbling geometries
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Notes on Relevant, Irrelevant, Marginal and Extremal Double Trace Perturbations
• Correlation functions of the ABJM model
• Holographic Renormalization for Fermions in Real Time
• Towards a consistent AdS/QCD dictionary
• Soft Wall holographic model for the minimal Composite Higgs
• Exact solutions for scalars and spinors on quantized (Euclidean) $Ad{S}_2$ and the correspondence principle
• Gauge Dependence in the AdS/CFT Correspondence
• Bulk equations of motion from CFT correlators
• The Hadamard Function and the Feynman Propagator in the AdS/CFT Correspondence
• Sine-Gordon Theory : Entanglement entropy and holography
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Regular and irregular boundary conditions in AdS/CFT correspondence for spinor field
• Holographic Beta functions for the Generalized Sine Gordon Theory
• Structure constants of $\beta$ deformed super Yang-Mills
• A note on the perturbative properties of BPS operators
• Non-extremal Island in de Sitter Gravity
• On the semiclassical 3-point function in AdS_3
• Aspects of the Holographic Study of Flavor Dynamics
• OPE between the energy-momentum tensor and the Wilson loop in N=4 Super-Yang-Mills theory
• Holographic RG flow triggered by a classically marginal operator
• In-medium effects in the holographic quark-gluon plasma
• "Old" Conformal Bootstrap on AdS: $O(N)$ symmetric scalar model
• Introduction to Gauge/Gravity Duality (TASI Lectures 2017)
• Cubic interactions in the BMN limit of AdS(3) x S(3)
• Quantum Gravity and the Holographic Principle
• Quantization of a Scalar Field in Two Poincaré Patches of Anti-de Sitter Space and AdS/CFT
• Two disjoint aspects of the deformation programme: quantizing Nambu mechanics; singleton physics
• Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension
• On the supermultiplet of anomalous currents in d=6
• A Holographic Constraint on Scale Separation
• Exact bosonic Matrix Product States (and holography)
• $W_4$ Toda example as hidden Liouville CFT
• Higgs-like (pseudo)Scalars in AdS${}_4$, Marginal and Irrelevant Deformations in CFT_3 and Instantons on S^3
• Proper time to singularity and thermal correlators
• Quantization in Ads and the Ads/CFT Correspondence
• UV-finite "old" conformal bootstrap on AdS: scalar case
• Supersymmetric Localization in AdS${}_5$ and the Protected Chiral Algebra
• Holographic derivation of a class of short range correlation functions
• Three point functions and the effective lagrangian for the chiral primary fields in D=4 supergravity on AdS2 x S2
• Flat Holography & Holographic Renormalization: Scalar Field
• Jet Physics from Static Charges in AdS
• Undecidability in Spacetime Geometry via the AdS/CFT Correspondence
• Comment on Field Redefinitions in the AdS/CFT Correspondence
• Universal properties of the U(1) current at deconfined quantum critical points: comparison with predictions from gauge/gravity duality
• AdS/CFT correspondence via R-current correlation functions revisited
• Full S-matrices and Witten diagrams with (relative) L-infinity algebras
• B-type anomaly coefficients for the D3-D7 domain wall
• Toward Holography on Biregular Trees
• How to Succeed at Witten Diagram Recursions without Really Trying
• Noncommutative $Ad{S}_2$ II: The Correspondence Principle
• Finite size effect on quantum correlations
• Logarithmic operators in SL(2, R) WZNW model, Singletons and AdS_3/(L)CFT_2 correspondence
• On the Role of Boundary Terms in the AdS/CFT Correspondence
• Flat limit of massless scalar scattering in ${\mathrm{AdS}}_2$
• Spinor vertexes and bubbles in the "old" conformal bootstrap on AdS and FMH problem: Yukawa model
• On the Stress Tensor Light-ray Operator Algebra
• Thermal R-current correlators from AdS/CFT correspondence
• Holographic Operator Product Expansion of Loop Operators in $\mathcal{N}=4$ $SO(N)$ Super Yang-Mills Theory
• Noncommutative $Ad{S}_2$ I: Exact solutions
• Entanglement and Excitations in Gauge/Gravity Duality
• Three-point functions of semiclassical string states and conserved currents in AdS_4 x CP^3
• Spacetime Bananas with EOW Branes and Spins
• Thermodynamic Split Conjecture and an Observational Test for Cosmological Entropy
• "Old" Conformal Bootstrap in the AdS/CFT Context
• Three-point current correlation functions as probes of Effective Conformal Theories
• Two applications of the analytic conformal bootstrap: A quick tour guide
• Boundary fermion currents and subleading order chiral anomaly in the AdS/CFT correspondence
• Dressing in AdS and a Conformal Bethe-Salpeter Equation
• Exact chiral ring of AdS(3)/CFT(2)
• AdS space compactification and holographic mapping in the AdS/CFT correspondence
• Near-AdS${}_2$ Spectroscopy: classifying the spectrum of operators and interactions in $\mathcal{N}=2$ 4D supergravity
• Beyond the tree level in the AdS/CFT Correspondence
• P-Branes Dynamics, AdS/CFT and Correlation Functions
• A Note on Scalar Field Theory in AdS_3/CFT_2
• Background field and time dependence effects in holographic models
• De Sitter scattering amplitudes in the Born approximation
• Branes and Brane Worlds in M-Theory
• The Intermediate Coupling Regime in the AdS/CFT Correspondence
• Tenfold Way for Holography : AdS/CFT and Beyond