Helicity basis for three-dimensional conformal field theory

Three-point correlators of spinning operators admit multiple tensor structures compatible with conformal symmetry. For conserved currents in three dimensions, we point out that helicity commutes with conformal transformations and we use this to construct three-point structures which diagonalize helicity. In this helicity basis, OPE data is found to be diagonal for mean-field correlators of conserved currents and stress tensor. Furthermore, we use Lorentzian inversion formula to obtain anomalous dimensions for conserved currents at bulk tree-level order in holographic theories, which we compare with corresponding flat-space gluon scattering amplitudes.

Automated summary

Three-point correlators of spinning operators in three dimensions have multiple tensor structures compatible with conformal symmetry. Helicity commutes with conformal transformations for conserved currents, allowing for the construction of three-point structures that diagonalize helicity. Using the Lorentzian inversion formula, anomalous dimensions for conserved currents at bulk tree-level order are obtained and compared with flat-space gluon scattering amplitudes.