Scalar scattering via conformal higher spin exchange

Understand

Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries.

• We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space.
• We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes (modulo delta-function terms having support on measure-zero domain in phase space).
• Independently, we show that this vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model.