Supergravity with cosmological constant and the AdS group

TL;DR

This paper constructs a supergravity action in four dimensions with a cosmological constant that is invariant under the AdS supergroup, ensuring off-shell closure of supersymmetry without auxiliary fields.

Contribution

It introduces a supersymmetric extension of the Stelle-West formalism to build an invariant supergravity action under the AdS group in four dimensions.

Findings

The action is genuinely invariant under the AdS supergroup.

Supersymmetry algebra closes off shell without auxiliary fields.

The Poincaré supergravity limit is also discussed.

Abstract

It is shown that the supersymmetric extension of the Stelle-West formalism permits the construction of an action for $(3+1)$-dimensional N=1 supergravity with cosmological constant genuinely invariant under the $OSp(4/1).$ Since the action is invariant under the supersymmetric extension of the $AdS$ group, the supersymmetry algebra closes off shell without the need for auxiliary fields. The limit case $m\to 0$, i.e.$(3+1)$ -dimensional N=1 supergravity invariant under the Poincar\'{e} supergroup is also discussed.