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

TL;DR

This paper proves that under certain conditions, N=1 D=4 supergravity is the unique consistent theory combining a massless spin 2 and spin 3/2 field, using BRST cohomology techniques without assuming general covariance.

Contribution

It demonstrates the uniqueness of N=1 D=4 supergravity as the only consistent interaction between these fields under specified assumptions, without requiring general covariance.

Findings

N=1 D=4 supergravity is uniquely consistent under the given conditions.

Supersymmetry invariance emerges automatically from the analysis.

Various cohomologies related to conservation laws are identified.

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, Poincar\'e 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.