Double copy structure of parity-violating CFT correlators

TL;DR

The paper establishes that general parity-violating three-dimensional CFTs exhibit a double-copy structure in momentum-space three-point correlators of conserved currents, the stress tensor, and marginal scalars. By decomposing correlators into homogeneous and non-homogeneous pieces, the authors show that double-copy relations hold separately for each part and extend the framework to higher-spin currents, where spin-s correlators can be viewed as s copies of spin-1 correlators. The results are corroborated through both momentum-space CFT calculations and tree-level $dS_4$ Feynman diagrams, with consistent flat-space limits that connect to standard scattering amplitudes. The work also demonstrates explicit amplitude-level double copies in parity-violating theories and discusses generalizations to higher points and OPE data, highlighting a deep link between CFT structure and gravitational/gauge-theory double-copy ideas.

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 $dS_4$. 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.