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A note on the uniqueness of D=4 N=1 Supergravity

Nicolas Boulanger·Mboyo Esole
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Abstract

We investigate in 4 spacetime dimensions, all the consistent deformations of the lagrangian ${\cal L}_2+{\cal L}_{3/2}$, which is the sum of the Pauli-Fierz lagrangian ${\cal L}_2$ for a free massless spin 2 field and the Rarita-Schwinger lagrangian ${\cal L}_{3/2}$ 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 conservations laws are also given.

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Nicolas Boulanger, Mboyo Esole. 2002-05-07. A note on the uniqueness of D=4 N=1 Supergravity. https://doi.org/10.1088/0264-9381%2F19%2F8%2F304

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