On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators

Abstract

The AdS boundary correlators and their dual correlation functions of boundary operators have been the main dynamic observables of the holographic duality relating a bulk AdS theory and a boundary conformal field theory. We show that tree-level AdS boundary correlators for generic states can be expressed as nonlocal differential operators of a certain structure acting on contact Witten diagrams. We further write the boundary correlators in a form that is very similar to flat space amplitudes, with Mandelstam variables replaced by certain combinations of single-state conformal generators, prove that all tree-level AdS boundary correlators have a differential representation, and detail the conversion of such differential expressions to position space. We illustrate the construction through the computation of the boundary correlators of scalars coupled to gluons and gravitons; when converted to position space, they reproduce known results. Color-kinematics duality and BCJ relations can be defined in analogy with their flat space counterparts, and are respected by the scalar correlators with a gluon exchange. We also discuss potential approaches to the double copy and find that its direct generalization may require nontrivial extensions.

50 pages; v2: references added, matching published version

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Cited by in corpus (19)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• New recursions for tree-level correlators in (Anti) de Sitter space
• Analytical evaluation of AdS${}_4$ Witten diagrams as flat space multi-loop Feynman integrals
• BCJ relations in ${AdS}_5\times S^3$ and the double-trace spectrum of super gluons
• Non-perturbative Double Copy in Flatland
• Effective Field Theories and Cosmological Scattering Equations
• Enhanced Soft Limits in de Sitter Space
• Soft limits of the wavefunction in exceptional scalar theories
• Spinning correlators in $\mathcal{N}=2$ SCFTs: Superspace and AdS amplitudes
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• A Type of Unifying Relation in (A)dS Spacetime
• Flat-space structure of gluon and graviton in AdS
• Bootstrapping Witten diagrams via differential representation in Mellin space
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Double copy for tree-level form factors. Part II. Generalizations and special topics
• Soft Limits of Gluon and Graviton Correlators in Anti-de Sitter Space
• 4D Flat-space scattering amplitude /$CF{T}_3$ correlator correspondence revisited
• Hawking radiation from the double copy
• A Novel On-Shell Recursive Relation