Supergravity and the Poincare group

TL;DR

This paper proposes a 3+1-dimensional supergravity action that is genuinely invariant under the Poincare supergroup, ensuring off-shell closure of the supersymmetry algebra without auxiliary fields.

Contribution

It introduces a supergravity action invariant under the Poincare supergroup with off-shell supersymmetry closure, avoiding auxiliary fields.

Findings

The action is invariant under local Lorentz and Poincare transformations.

Supersymmetry algebra closes off-shell without auxiliary fields.

The construction ensures off-shell invariance under the Poincare supergroup.

Abstract

An action for 3+1-dimensional supergravity genuinely invariant under the Poincare supergroup is proposed. The construction of the action is carried out considering a bosonic lagrangian invariant under both local Lorentz rotations and local Poincare translations as well as under diffeomorphism, and therefore the Poincare algebra closes off-shell. Since the lagrangian is invariant under the Poincare supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.