Abstract
We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.
Highlights
There has been a remarkable confluence in the study of CFT correlators and scattering amplitudes in recent years
We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators
One of the interesting relationships that exists for flat space scattering amplitudes is the double-copy relation between gauge theory and gravity amplitudes, and the associated color-kinematics duality [10,11,12]
Summary
There has been a remarkable confluence in the study of CFT correlators and scattering amplitudes in recent years. In this paper we will demonstrate double copy relations between general parity-violating CF T3 3-point correlators involving marginal scalars, spin one and spin two conserved currents. We will show that double copy relations hold even with the inclusion of the parity violating contributions We demonstrate this using the results for parity even CFT correlators from [20, 27, 29, 33] and parity odd correlators from [61, 71], where CFT correlators were obtained by solving conformal Ward identities. Appendix E contains a few details regarding some constraints on OPE coefficients arising from double copy relations
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