Constraining conformal field theory with higher spin symmetry in four dimensions

TL;DR

This paper demonstrates that in four-dimensional conformal field theories with higher spin symmetry, stress-energy tensor correlators are highly constrained, leading to the conclusion that such theories are essentially free fields.

Contribution

It shows that higher spin symmetry restricts stress-energy tensor correlators to be linear combinations of free field solutions, implying these theories are free.

Findings

Correlators have at most double pole singularities.

4-, 5-, and 6-point functions are linear combinations of free field correlators.

Theories with higher spin symmetry are essentially free.

Abstract

We analyze the constraints on the general form and the singularity structure of the correlation functions of the symmetric, traceless and conserved stress-energy tensor implied by conformal invariance and higher spin symmetry in four dimensions. In particular, we show that all these correlation functions will have at most double pole singularities. We then compute the 4-, 5- and 6-point functions of the stress-energy tensor and find that they are linear combinations of the three free field expressions (scalar, fermion and Maxwell field). This is a strong indication that all such theories are essentially free.