Abstract
We study contact four-point amplitudes in the spinor-helicity formalism in anti-de Sitter space. We find that these amplitudes can be brought to an especially simple form, which we call canonical. Next, we classify consistent contact amplitudes by requiring correct transformation properties with respect to the AdS isometry algebra. Finally, we establish a connection between the canonical form of AdS amplitudes and scalar multi-trace conformal primaries in flat space.
Highlights
We study contact four-point amplitudes in the spinor-helicity formalism in anti-de Sitter space
One can note that (3.10) has one more property: the power of the Goperator acting on the delta function is twice the degree of the polynomial in the Mandelstam variables that appears in the prefactor
The key difference of this computation with its flat space counterpart is that due to the absence of translation invariance in AdS space, the action manifestly depends on space-time coordinates, and, as a result, amplitudes involve derivatives of the momentum-conserving delta function
Summary
We collect some useful results on the spinor-helicity formalism in AdS4. By taking the flat space limit R → ∞, we recover the usual Poincare algebra in the spinor form. This representation of the AdS isometry algebra is often referred to as the twisted adjoint representation and is used extensively in the higher-spin literature [30]. The AdS space counterpart of the flat plane-wave solutions in the scalar case are given by φ = Geipx with p2 = 0. By taking the limit R → ∞ of (2.6), we reproduce the familiar flat-space plane waves. AdS plane waves (2.6) will be used to calculate some lower-derivative four-point amplitudes
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