A note on the uniqueness of <i>D</i> = 4, <i>N</i> = 1 supergravity

Abstract

We investigate in 4 spacetime dimensions, all the consistent deformations of\nthe lagrangian ${\\cal L}_2+{\\cal L}_{{3/2}}$, which is the sum of the\nPauli-Fierz lagrangian ${\\cal L}_2$ for a free massless spin 2 field and the\nRarita-Schwinger lagrangian ${\\cal L}_{{3/2}}$ for a free massless spin 3/2\nfield. Using BRST cohomogical techniques, we show, under the assumptions of\nlocality, Poincar\\'e invariance, conservation of the number of gauge symmetries\nand the number of derivatives on each fields, that N=1 D=4 supergravity is the\nonly consistent interaction between a massless spin 2 and a massless spin 3/2\nfield. We do not assume general covariance. This follows automatically, as does\nsupersymmetry invariance. Various cohomologies related to conservations laws\nare also given.\n