The Superalgebraic Approach to Supergravity

TL;DR

The paper recasts four-dimensional N=1 supergravity as a partially compensated gauge theory of OSp(1|4) using a compensator field, building on a gauge-theoretic view of gravity with Sp(4,R). By translating to spinor language and employing graded algebras, it derives a MacDowell-Mansouri–type action and demonstrates a hidden local supersymmetry that arises from the gauge structure. It further introduces projector operators to separate Lorentz and SUSY sectors, showing how the action decomposes into topological, kinetic, and cosmological-constant pieces, and proves that pure supergravity without a cosmological term is obtainable within this framework. The work argues that gravity and supergravity can be elegantly formulated as gauge theories with a decoupled vacuum algebra, offering a path toward superspace formulations and potential extensions with additional coordinates.

Abstract

We formulate classical actions for N=1 supergravity in D=(1,3) as a gauge theory of OSp(1|4). One may choose the action such that it does not include a cosmological term.