Recursion Relations for AdS/CFT Correlators

Abstract

We expand on the results of arXiv:1011.0780 where we presented new recursion relations for correlation functions of the stress tensor and conserved currents in conformal field theories with an AdS_p dual for p > 4. These recursion relations are derived by generalizing the Britto-Cachazo-Feng-Witten (BCFW) relations to amplitudes in anti-de Sitter space (AdS) that are dual to boundary correlators, and are usually computed perturbatively by Witten diagrams. Our results relate vacuum-correlation functions to integrated products of lower-point transition amplitudes, which correspond to correlators calculated between states dual to certain normalizable modes. We show that the set of polarization vectors for which amplitudes behave well under the BCFW extension is smaller than in flat-space. We describe how transition amplitudes for more general external polarizations can be constructed by combining answers obtained by different pairs of BCFW shifts. We then generalize these recursion relations to supersymmetric theories. In AdS, unlike flat-space, even maximal supersymmetry is insufficient to permit the computation of all correlators of operators in the same multiplet as a stress-tensor or conserved current. Finally, we work out some simple examples to verify our results.

45 pages

References in corpus (46)

• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• Perturbative Gauge Theory As A String Theory In Twistor Space
• New Recursion Relations for Tree Amplitudes of Gluons
• An Index for 4 dimensional Super Conformal Theories
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Hard Scattering and Gauge/String Duality
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• What is the Simplest Quantum Field Theory?
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Holographic Probes of Anti-de Sitter Spacetimes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• A Duality For The S Matrix
• Direct extraction of one-loop integral coefficients
• Dual Superconformal Invariance, Momentum Twistors and Grassmannians
• On Tree Amplitudes in Gauge Theory and Gravity
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Towards a Basis for Planar Two-Loop Integrals
• Precise Predictions for W + 3 Jet Production at Hadron Colliders
• On Four-point Functions in the CFT/AdS Correspondence
• The S-Matrix in Twistor Space
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• W+3 jet production at the Tevatron
• What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
• BCFW for Witten Diagrams
• Scattering Amplitudes and BCFW Recursion in Twistor Space
• On-shell Recursion in String Theory
• W+3 jet production at the LHC as a signal or background
• MHV, CSW and BCFW: field theory structures in string theory amplitudes
• BCFW Recursion Relations and String Theory
• The Next-to-Simplest Quantum Field Theories
• The Spectrum of Yang Mills on a Sphere
• Superconformal Invariants or How to Relate Four-point AdS Amplitudes
• On time-dependent AdS/CFT
• The Noncommutative S-Matrix
• F(4) Supergravity and 5D Superconformal Field Theories
• Rational Terms in Theories with Matter

Cited by in corpus (49)

• Spinning Conformal Blocks
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators
• The super-correlator/super-amplitude duality: Part I
• Linking the Singularities of Cosmological Correlators
• Diffractive photoproduction of $J/\psi$ and ${\rm Y}$ using holographic QCD: gravitational form factors and GPD of gluons in the proton
• On Higher Spin Gauge Theory and the Critical O(N) Model
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The Inflationary Wavefunction from Analyticity and Factorization
• On duality of color and kinematics in (A)dS momentum space
• Color/Kinematics Duality in AdS${}_4$
• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• $J/\psi$ near threshold in holographic QCD: A and D gravitational form factors
• On Feynman rules for Mellin amplitudes in AdS/CFT
• CFT Unitarity and the AdS Cutkosky Rules
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• Cosmological Scattering Equations
• Twistor Strings for N=8 Supergravity
• An étude of momentum space scalar amplitudes in AdS
• On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators
• The graviton four-point function in de Sitter space
• On NMHV form factors in N=4 SYM theory from generalized unitarity
• An Introduction to On-shell Recursion Relations
• Loops in AdS: From the Spectral Representation to Position Space
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Cosmological Scattering Equations at Tree-level and One-loop
• On spinning loop amplitudes in Anti-de Sitter space
• Dispersion Formulas in QFTs, CFTs, and Holography
• New recursions for tree-level correlators in (Anti) de Sitter space
• Opacity from Loops in AdS
• On-shell supersymmetry for massive multiplets
• Gravity with a cosmological constant from rational curves
• Correlation functions of local composite operators from generalized unitarity
• Effective Field Theories and Cosmological Scattering Equations
• Loops in AdS: From the Spectral Representation to Position Space II
• Enhanced Soft Limits in de Sitter Space
• Three particle superstring amplitudes with massive legs
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• A Type of Unifying Relation in (A)dS Spacetime
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Recursion Relations in $p$-adic Mellin Space
• 1/N corrections to $F_1$ and $F_2$ structure functions of vector mesons from holography
• Neutrino-nucleon DIS from Holographic QCD: PDFs of sea and valence quarks, form factors, and structure functions of the proton
• Unimodular gravity and the gauge/gravity duality
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• On the consistency of (partially-)massless matter couplings in de Sitter space
• How to Succeed at Witten Diagram Recursions without Really Trying