On triviality of S-matrix in conformal higher spin theory

TL;DR

This paper investigates the conformal higher spin (CHS) theory in four dimensions, demonstrating that all tree-level scattering amplitudes vanish due to the underlying higher spin symmetry, indicating a trivial S-matrix.

Contribution

It explicitly computes interaction vertices and tree-level scattering amplitudes in CHS theory, showing their vanishing and highlighting the role of higher spin symmetry in trivializing the S-matrix.

Findings

All computed tree-level 4-particle scattering amplitudes vanish.

The vanishing of amplitudes extends to all scattering processes in CHS theory.

Higher spin symmetry underpins the triviality of the S-matrix in this framework.

Abstract

We consider the conformal higher spin (CHS) theory in d=4 that contains the s=1 Maxwell vector, s=2 Weyl graviton and their higher spin s=3,4,... counterparts with higher-derivative \box^s kinetic terms. The interacting action for such theory can be found as the coefficient of the logarithmically divergent part in the induced action for sources coupled to higher spin currents in a free complex scalar field model. We explicitly determine some cubic and quartic interaction vertices in the CHS action from scalar loop integrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11 -> 11, 22 -> 22 and 11 -> 22 and find that after summing up all the intermediate CHS exchanges they vanish. This generalises the vanishing of the scattering amplitude for external conformal scalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896. This vanishing should generalise to all scattering amplitudes in the CHS theory and as in the conformal scalar scattering case should be a consequence of the underlying infinite dimensional higher spin symmetry that extends the standard conformal symmetry.