Spinor-helicity formalism for massless fields in AdS4. Part II. Potentials

Abstract

In a recent letter we suggested a natural generalization of the flat-space spinorhelicity 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.

Spinor-helicity formalism for massless fields in AdS4 III: contact four-point amplitudes

“…In this section, we collect some useful results on the spinor-helicity formalism in AdS 4 . For more comprehensive review and references, we refer the reader to [4,5]. Our conventions are collected in appendix A.…”

“…One thing that one can learn from example (3.8) is that derivatives of the delta function, that are contracted with momenta of fields on external lines can be eliminated. Such terms were absent for three-point amplitudes [4,5] and it seems natural to try to achieve their absence for four-point amplitudes as well. Another feature inherent to three-point amplitudes is that derivatives of the momentum-conserving delta function always appear in combinationG.…”

“…In this section, we will use symmetry arguments to construct all contact four-point amplitudes of scalar fields. Analogous arguments were used in [5] to classify three-point amplitudes of spinning fields.…”

“…Thanks to these virtues, the spinor-helicity formalism has become an important part of modern amplitude methods; for review see [1][2][3]. Aiming to achieve similar simplifications for computations that appear in the context of holography and higher-spin theories, we recently extended the spinor-helicity formalism to fourdimensional anti-de Sitter space [4,5]. 1 In particular, we constructed the AdS 4 counterpart of the plane-wave solutions for spinning fields and then employed them to evaluate some spinning three-point amplitudes.…”

“…Moreover, there is an alternative spinor-helicity formalism for AdS4 suggested in[8]. For a more comprehensive review of the relation of our formalism to other approaches, see[5].…”