Abstract
In this Letter, we suggest a natural spinor-helicity formalism for massless fields in four-dimensional anti-de Sitter space (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,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.
Highlights
Introduction.—The spinor-helicity formalism has established itself as the most efficient framework for representing on-shell scattering amplitudes of massless particles in the 4D Minkowski space; see, e.g., [1,2] for reviews
In this Letter, we make an alternative proposal for the spinor-helicity formalism in four-dimensional anti–de Sitter space (AdS4), which has all features of the flat space formalism and, in particular, reduces to the latter for conformal theories [12]
It is worth mentioning the twistor approach [13], which is naturally adapted to describing fields in conformally flat spaces
Summary
Introduction.—The spinor-helicity formalism has established itself as the most efficient framework for representing on-shell scattering amplitudes of massless particles in the 4D Minkowski space; see, e.g., [1,2] for reviews. We classify all consistent three-point amplitudes for massless particles in AdS4 using the spinor-helicity formalism and find agreement with [34]. Once plane wave solutions Eq (1) are available, one can Published by the American Physical Society evaluate amplitudes using the Feynman rules in any theory of massless fields.
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