Spinning Conformal Correlators

TL;DR

This paper introduces an embedding formalism for conformal field theories that simplifies computations of tensor structures in correlation functions, enabling efficient analysis of operators with arbitrary spin.

Contribution

It develops an index-free, polynomial-based notation for symmetric traceless tensors, facilitating calculations and revealing a correspondence with scattering amplitudes in higher dimensions.

Findings

Efficient computation of tensor structures in conformal correlators.

Simplified constraints for tensor conservation.

Matching of conformal correlator structures with higher-dimensional scattering amplitudes.

Abstract

We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.