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 mathfrak {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.
Highlights
As it is well known, a good candidate for describing dark energy is the cosmological constant
The Maxwell and Ad S–Lorentz algebras of all types, together with their supersymmetric extensions, have found interesting applications ingravity, the new generators still require a clearer physical interpretation, concerning the presence of extra fermionic generators in the supersymmetric cases
Driven by the fact that from Ad S–Lorentz typealgebras one can introduce the cosmological term ingravity in the presence of an extra bosonic generator Zab [28,39], we have presented a new supersymmetrization of the Ad S–Lorentz algebra Ad S − L4 of [28]
Summary
As it is well known, a good candidate for describing dark energy is the cosmological constant (see, for example, [1,2]). Since it contains Ad S − L4 as a bosonic subalgebra, in this sense (2.9) it could be viewed as the minimal supersymmetrization of a minimal Maxwell-like algebra (that is, a deformation of the Maxwell algebra M, see [18]) in which the bosonic generator Zab is non-abelian ([Zab, Zcd ] = ηbc Zad − ηac Zbd − ηbd Zac + ηad Zbc) and where [Zab, Pc] = ηbc Pa−ηac Pb, even if the generators Zab, in this case, do not behave as Lorentz generators when considering the supersymmetric extension and the corresponding commutation relations with the fermionic charges In this context, we observe that the behavior of the generators Zab in s Ad S − L4 is different from the behavior of the Zab’s in (a contraction of) the generalized minimal Ad S–Lorentz superalgebra of [39]. In order to construct an action based on s Ad S − L4 we start, on the same lines of [38,39], from the following 1-form connection: A
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