Double copy structure of CFT correlators

TL;DR

The paper demonstrates that momentum-space 3-point CFT correlators in odd dimensions encode a double-copy structure linking gauge-theory and gravity amplitudes in one higher dimension. By solving conformal Ward identities and analyzing the flat-space limit via triple-K integrals, the authors show that ⟨JJJ⟩, ⟨TTT⟩, ⟨JJ𝒪⟩, and ⟨TT𝒪⟩ decompose into combinations of YM, F^3, φR^2, and W^3 amplitudes related by double-copy relations; in d=3, tensor degeneracies and a de Sitter perspective further illuminate these connections and extend the double-copy structure beyond the strict flat-space limit. The work provides compact, spinor-helicity formalism expressions and identifies explicit amplitude correspondences, including YM-dilaton and graviton-scalar sectors, suggesting potential worldsheet or polytope interpretations in holography. Overall, it strengthens the bridge between holographic CFT data and bulk scattering amplitudes, with implications for bootstrap techniques and inflationary cosmology.

Abstract

We consider the momentum-space 3-point correlators of currents, stress tensors and marginal scalar operators in general odd-dimensional conformal field theories. We show that the flat space limit of these correlators is spanned by gauge and gravitational scattering amplitudes in one higher dimension which are related by a double copy. Moreover, we recast three-dimensional CFT correlators in terms of tree-level Feynman diagrams without energy conservation, suggesting double copy structure beyond the flat space limit.

Figures (1)

• Figure 1: Tree-level diagrams for 3-point correlators. The first diagram describes $W^3$ and $F^3$ interactions, while the second diagram describes $\phi F^2$ and $\phi W^2$ interactions.