Generalized supersymmetric cosmological term in N=1 Supergravity

TL;DR

This paper introduces a new geometric formulation of N=1 supergravity incorporating a generalized supersymmetric cosmological constant using the $AdS$-Lorentz superalgebra, extending previous models with a novel algebraic approach.

Contribution

It presents a geometric supergravity model based solely on $AdS$-Lorentz superalgebra curvatures, generalizing the supersymmetric cosmological term in N=1 supergravity.

Findings

Constructs a supergravity action from $AdS$-Lorentz superalgebra curvatures.

Demonstrates a MacDowell-Mansouri like formulation for N=1 supergravity.

Extends the algebraic framework to a generalized $AdS$-Lorentz superalgebra.

Abstract

An alternative way of introducing the supersymmetric cosmological term in a supergravity theory is presented. We show that the $AdS$-Lorentz superalgebra allows to construct a geometrical formulation of supergravity containing a generalized supersymmetric cosmological constant. The $N=1$, $D=4$ supergravity action is built only from the curvatures of the $AdS$-Lorentz superalgebra and corresponds to a MacDowell-Mansouri like action. The extension to a generalized $AdS$-Lorentz superalgebra is also analyzed.