Generalized cosmological term in D=4 supergravity from a new AdS-Lorentz superalgebra

TL;DR

This paper introduces a new superalgebra-based approach to construct a D=4 supergravity action with a generalized cosmological term, expanding the AdS-Lorentz algebra and ensuring gauge invariance and supersymmetry.

Contribution

It presents a novel supersymmetrization of the AdS-Lorentz algebra using an abelian semigroup expansion, leading to a new supergravity action with a generalized cosmological term.

Findings

Constructed a D=4 supergravity action from a new superalgebra.

Demonstrated gauge invariance and supersymmetry of the action.

Provided a geometric derivation of the generalized cosmological term.

Abstract

A new supersymmetrization of the so-called AdS-Lorentz algebra is presented. It involves two fermionic generators and is obtained by performing an abelian semigroup expansion of the superalgebra osp(4|1). The peculiar properties of the aforesaid expansion method are then exploited to construct a D=4 supergravity action involving a generalized supersymmetric cosmological term in a geometric way, only from the curvatures of the novel superalgebra. The action obtained with this procedure is a MacDowell-Mansouri like action. Gauge invariance and supersymmetry of the action are also analyzed.