On duality of color and kinematics in (A)dS momentum space

Abstract

We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS${}_4$ and the second for the integrand in general AdS${}_{d+1}$. For the integrated correlator, we find color-kinematics does not yield additional relations among $n$-point, color-ordered correlators. To study color-kinematics for the AdS${}_{d+1}$ Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdS${}_{d+3}$ to Yang-Mills in AdS${}_{d+1}$. We also find a double-copy relation at three-points between Yang-Mills in AdS${}_{d+1}$ and gravity in AdS${}_{d-1}$ and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

14 pages, 4 figures, v2: Added references and footnote for double-copy

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• Loops in AdS: From the Spectral Representation to Position Space
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• One-loop Gluon Amplitudes in AdS
• Super Gluon Five-Point Amplitudes in AdS Space
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Momentum space parity-odd CFT 3-point functions
• Cosmological Scattering Equations at Tree-level and One-loop
• Helicity basis for three-dimensional conformal field theory
• Dispersion Formulas in QFTs, CFTs, and Holography
• Towards Color-Kinematics Duality in Generic Spacetimes
• New recursions for tree-level correlators in (Anti) de Sitter space
• A handbook of holographic 4-point functions
• Continuous Spectrum on Cosmological Collider
• Full-color three-loop three-point form factors in N=4 SYM
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Non-perturbative Double Copy in Flatland
• Exceptional scalar theories in de Sitter space
• Effective Field Theories and Cosmological Scattering Equations
• Loops in AdS: From the Spectral Representation to Position Space II
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• Enhanced Soft Limits in de Sitter Space
• Soft limits of the wavefunction in exceptional scalar theories
• Analytic Formulae for Inflationary Correlators with Dynamical Mass
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• One-loop multicollinear limits from 2-point amplitudes on self-dual backgrounds
• Differential Operators and Unifying Relations for 1-loop Feynman Integrands from Berends-Giele Currents
• Flat-space structure of gluon and graviton in AdS
• Shift operators from the simplex representation in momentum-space CFT
• Bootstrapping Witten diagrams via differential representation in Mellin space
• MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch
• Double copy for tree-level form factors. Part II. Generalizations and special topics
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• Next-to-MHV Yang-Mills kinematic algebra
• On the consistency of (partially-)massless matter couplings in de Sitter space
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Hawking radiation from the double copy
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Analytic Studies of Fermions in the Conformal Bootstrap
• Twisted de Rham theory for string double copy in AdS