Spinor-Helicity Formalism for Massless Fields in AdS$_4$ II: Potentials

TL;DR

This work extends the flat-space spinor-helicity formalism to AdS$_4$ by developing plane-wave representations for both field strengths and their potentials, and by computing three-point amplitudes without internal lines. It introduces the twisted-adjoint (AdS) representation, derives AdS plane waves, and demonstrates how potentials can be fixed in a gauge that preserves transversality to a null vector, enabling genuine AdS amplitudes for spins up to two. The authors classify all consistent three-point amplitudes in AdS$_4$ via symmetry considerations, revealing four independent structures analogous to flat-space results but with AdS-specific patching, and they introduce helicity-changing operators that generate related amplitudes. The results illuminate the AdS/flat-space correspondence for massless higher-spin interactions, offering a new framework to study holographic correlators and potential connections to chiral higher-spin theories and twistor methods. This formalism provides a practical, on-shell approach to AdS amplitudes, with clear paths to higher-point functions and holographic reconstruction.

Abstract

In a recent letter we suggested a natural generalization of the flat-space spinor-helicity formalism in four dimensions to anti-de Sitter space. In the present paper we give some technical details that were left implicit previously. For lower-spin fields we also derive potentials associated with the previously found plane wave solutions for field strengths. We then employ these potentials to evaluate some three-point amplitudes. This analysis illustrates a typical computation of an amplitude without internal lines in our formalism.