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

TL;DR

The paper addresses how to extend the 4d spinor-helicity formalism to massless fields in AdS$_4$ by exploiting a twisted-adjoint realization of the $so(3,2)$ isometry on $sl(2,\mathbb{C})$ spinor variables. It introduces AdS plane waves that intertwine spinor-helicity and spacetime representations and uses them to compute simple amplitudes, then classifies all consistent 3-point amplitudes by symmetry, revealing four parity-invariant structures whose realization depends on AdS patching. Explicit AdS plane-wave solutions and distributional kernels are derived, enabling a local, symmetry-driven construction of 3-point amplitudes that reproduce flat-space results in the appropriate limit and respect conformal invariance. The work provides a self-contained, on-shell framework for AdS$_4$ massless interactions with potential implications for holography, higher-spin theory, and the development of AdS on-shell methods, clarifying the relation between AdS and flat-space scattering data.

Abstract

In this letter we suggest a natural spinor-helicity formalism for massless fields in AdS${}_4$. It is based on the standard realization of the 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 AdS 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 to construct additional consistent interactions compared to approaches employing Lorentz tensors.