On triviality of S-matrix in conformal higher spin theory

TL;DR

This work investigates four-dimensional conformal higher spin theory, including an infinite tower of spins with higher-derivative kinetic terms, by deriving the induced CHS action from a free scalar CFT. The authors compute cubic and quartic CHS vertices from scalar-loop UV poles and analyze several tree-level 4-point amplitudes, showing that after summing exchanges of all CHS fields the amplitudes vanish in channels such as 11→11, 22→22, and 11→22. They reveal that the vanishing is tied to the infinite higher-spin symmetry extending conformal symmetry, and that the CHS S-matrix is likely trivial. The results generalize earlier findings for external scalars and point toward deep connections with HS symmetry, partial-wave structures via Jacobi polynomials, and potential AdS5/Higher-Spin dualities.

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.