No cross-interactions between the Weyl graviton and the massless Rarita-Schwinger field

Abstract

The proof of the fact that there are no nontrivial, consistent cross-couplings that can be added between the Weyl graviton and the massless Rarita-Schwinger field is accomplished by means of a cohomological approach, based on the deformation of the solution to the master equation from the antifield-Becchi-Rouet-StoraTyutin (BRST) formalism. The procedure developed here relies on the assumptions of locality, smoothness, (background) Lorentz invariance, Poincaré invariance, and preservation of the number of derivatives with respect to each field (the last hypothesis was made only in antighost number zero).

On the Uniqueness of D = 11 Interactions Among a Graviton, a Massless Gravitino and a Three-Form I: Pauli–fierz and Three-Form

“…[22]) and the 'interacting' part S ′h−A 1 , expressed by (78). In this section we investigate the consistency of the first-order deformation, described by equation (27). Along the same line as before, we can write the second-order deformation like the sum between the Pauli-Fierz contribution and the interacting part…”

“…[22] (or respectively Ref. [23]), and of cross-couplings among different Einstein gravitons in the presence of matter fields [22,24]- [27] has recently been shown by means of cohomological arguments. In the same context the uniqueness of D = 4, N = 1 supergravity was proved in Ref.…”