Abstract
We investigate in four spacetime dimensions, all the consistent deformations of the Lagrangian ℒ2 + ℒ3/2 , which is the sum of the Pauli–Fierz Lagrangian ℒ2 for a free massless spin-2 field and the Rarita–Schwinger Lagrangian ℒ3/2 for a free massless spin-3/2 field.Using BRST-cohomogical techniques, we show, under the assumptions of locality, Poincaré invariance, conservation of the number of gauge symmetries and the number of derivatives on each fields, that N = 1, D = 4 supergravity is the only consistent interaction between a massless spin-2 and a massless spin-3/2 field. We do not assume general covariance. This follows automatically, as does supersymmetry invariance. Various cohomologies related to conservation laws are also given.
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