Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3

Abstract

We compute four point functions of the stress tensor and conserved currents in AdS_4/CFT_3 using bulk perturbation theory. We work at treel level in the bulk theory, which we take to be either pure gravity or Yang Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four point correlator with arbitrary external helicities and momenta. We verify that, precisely as conjectured in a companion paper, the Maximally Helicity Violating (MHV) amplitude of gravitons or gluons appears as the coefficient of a specified singularity in the MHV stress-tensor or current correlator. We comment on the remarkably simple analytic structure of our answers in momentum space.

44 pages. Zipped source includes a Mathematica notebook (v2) discussion section revised

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• The Inflationary Wavefunction from Analyticity and Factorization
• Conformal $n$-point functions in momentum space
• On duality of color and kinematics in (A)dS momentum space
• Color/Kinematics Duality in AdS${}_4$
• Cosmological Bootstrap in Slow Motion
• CFT Unitarity and the AdS Cutkosky Rules
• Holographic probes of collapsing black holes
• Multipoint correlators of conformal field theories: implications for quantum critical transport
• Conformal correlators as simplex integrals in momentum space
• An étude of momentum space scalar amplitudes in AdS
• On the four-point function of the stress-energy tensors in a CFT
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• MHV scattering of gluons and gravitons in chiral strong fields
• On spinning loop amplitudes in Anti-de Sitter space
• Helicity basis for three-dimensional conformal field theory
• Dispersion Formulas in QFTs, CFTs, and Holography
• Towards Color-Kinematics Duality in Generic Spacetimes
• Graviton scattering in self-dual radiative space-times
• Einstein supergravity amplitudes from twistor-string theory
• Compressible quantum phases from conformal field theories in 2+1 dimensions
• Opacity from Loops in AdS
• Gravity with a cosmological constant from rational curves
• Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence
• Holographic torus correlators of stress tensor in $Ad{S}_3/CF{T}_2$
• Three and Four Point Functions of Stress Energy Tensors in D=3 for the Analysis of Cosmological Non-Gaussianities
• Twistor actions for gauge theory and gravity
• KLT-Like Behaviour of Inflationary Graviton Correlators
• The Boostless Bootstrap and BCFW Momentum Shifts
• Flat-space structure of gluon and graviton in AdS
• MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch
• New Worldsheet Formulae for Conformal Supergravity Amplitudes
• Comments on scattering in massive gravity, vDVZ and BCFW
• On the consistency of (partially-)massless matter couplings in de Sitter space
• A Universal Formula for the Stress-Tensor Contribution to Scalar Four-Point Functions
• Operator Method and Recursion Relations for Inflationary Correlator
• Information Geometry and Holographic Correlators