Spinor-Helicity Formalism for Massless Fields in ${\mathrm{AdS}}_4$

In this Letter, we suggest a natural spinor-helicity formalism for massless fields in four-dimensional anti–de Sitter space (${\mathrm{AdS}}_4$). It is based on the standard realization of the ${\mathrm{AdS}}_4$ isometry algebra $so(3,2)$ in terms of differential operators acting on $sl(2,\mathbb{C})$ spinor variables. We start by deriving the anti–de Sitter counterpart of plane waves in flat space and then use them to evaluate simple scattering amplitudes. Finally, based on symmetry arguments, we classify all three-point amplitudes involving massless spinning fields. As in flat space, we find that the spinor-helicity formalism allows us to construct additional consistent interactions as compared to approaches employing Lorentz tensors.