Helicity basis for three-dimensional conformal field theory

TL;DR

This paper introduces a helicity basis for three-dimensional conformal field theories, simplifying the analysis of three-point correlators of spinning operators and enabling the calculation of anomalous dimensions in holographic models.

Contribution

It constructs a helicity basis that diagonalizes tensor structures in 3D CFTs and applies Lorentzian inversion to compute anomalous dimensions, linking CFT data with flat-space scattering amplitudes.

Findings

Helicity commutes with conformal transformations in 3D.

Diagonalization of OPE data in the helicity basis for mean-field correlators.

Calculation of anomalous dimensions matching flat-space gluon scattering amplitudes.

Abstract

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.