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.
Highlights
Closed string amplitudes [9]
This formulation is relevant for the study of inflationary non-Gaussianities, where scattering amplitudes can be obtained from the flat space limit of cosmological in-in correlators, which are in turn related holographically to boundary CFT correlators [20,21,22,23,24,25,26,27]
For a parity-invariant but otherwise general CFT with d > 3, we find that the flat space limit of current correlators is spanned by scattering amplitudes in ordinary and higher-derivative Yang-Mills theory, while the flat space limit of stress tensor correlators is spanned by amplitudes in Einstein, φR2 and Weyl-cubed gravity, where φR2 is a curvature-squared theory coupled to scalars which reduces to a certain non-minimal conformal gravity in four dimensions [44]
Summary
We begin with a review of some basic facts about scattering amplitudes that will be relevant later on. In general odd dimensions d > 3 we have seen that CFT correlators of currents, stress tensors, and marginal scalars exhibit a double copy structure via their flat space limit. The double copy predicts a nonzero graviton-graviton-scalar amplitude in the φR2 theory, which we show arises from the flat space limit of T T O where O is a marginal scalar operator For this calculation, we need to take into account a degeneracy of the form factor basis. We need to take into account a degeneracy of the form factor basis Another special feature of d = 3 is that CFT correlators can be derived from 3-point functions in dS4 which are equivalent to flat space Feynman diagrams without energy conservation, dressed by conformal time integrals. This result suggests the existence of a double copy structure beyond the flat space limit
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