Dra. Rodríguez-Durán, Evelyn

We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

We explore the supersymmetry invariance of a supergravity theory in the presence of a non-trivial boundary. The explicit construction of a bulk Lagrangian based on an enlarged superalgebra, known as AdS-Lorentz, is presented. Using a geometric approach we show that the supersymmetric extension of a Gauss-Bonnet like gravity is required in order to restore the supersymmetry invariance of the theory.

We explore the possibility of finding pure Lovelock gravity as a particular limit of a Chern-Simons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.

We present the construction of the D = 3 Chern–Simons supergravity action without cosmological constant from the minimal Maxwell superalgebra sM3. This superalgebra contains two Majorana fermionic charges and can be obtained from the osp(2|1) ⊗ sp(2) superalgebra using the abelian semigroup expansion procedure. The components of the Maxwell invariant tensor are explicitly derived.

The multi-vector generalization of a rigid, partially-broken N = 2 supersymmetric theory is presented as a rigid limit of a suitable gauged N = 2 supergravity with electric, magnetic charges and antisymmetric tensor fields. This on the one hand generalizes a known result by Ferrara, Girardello and Porrati while on the other hand allows to recover the multi-vector BI models of [4] from N = 2 supergravity as the end-point of a hierarchical limit in which the Planck mass first and then the supersymmetry breaking scale are sent to infinity. We define, in the parent supergravity model, a new symplectic frame in which, in the rigid limit, manifest symplectic invariance is preserved and the electric and magnetic Fayet-Iliopoulos terms are fully originated from the dyonic components of the embedding tensor. The supergravity origin of several features of the resulting rigid supersymmetric theory are then elucidated, such as the presence of a traceless SU(2)- Lie algebra term in the Ward identity and the existence of a central charge in the supersymmetry algebra which manifests itself as a harmless gauge transformation on the gauge vectors of the rigid theory; we show that this effect can be interpreted as a kind of “superspace non-locality” which does not affect the rigid theory on space-time. To set the stage of our analysis we take the opportunity in this paper to provide and prove the relevant identities of the most general dyonic gauging of Special-Kaehler and Quaternionic-Kaehler isometries in a generic N = 2 model, which include the supersymmetry Ward identity, in a fully symplectic-covariant formalism.

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.

We show that the Lagrangian for Lovelock–Cartan gravity theory can be reformulated as an action which leads to General Relativity in a certain limit. In odd dimensions the Lagrangian leads to a Chern–Simons theory invariant under the generalized Poincaré algebra B2n+1, while in even dimensions the Lagrangian leads to a Born–Infeld theory invariant under a subalgebra of the B2n+1 algebra. It is also shown that torsion may occur explicitly in the Lagrangian leading to new torsional Lagrangians, which are related to the Chern–Pontryagin character for the B2n+1 group.

We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sM4, which can be derived from the osp (4|1) superalgebra by applying the abelian semigroup expansion procedure. We show that N = 1, D = 4 pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra sM4. We extend this result to all minimal Maxwell superalgebras type sMm+2. The invariance under supersymmetry transformations is also analized.

Recently it was shown that standard odd- and even-dimensional general relativity can be obtained from a (2n + 1)-dimensional Chern–Simons Lagrangian invariant under the B2n+1 algebra and from a (2n)-dimensional Born–Infeld Lagrangian invariant under a subalgebra LB2n+1, respectively. Very recently, it was shown that the generalized Inönü–Wigner contraction of the generalized AdS–Maxwell algebras provides Maxwell algebras of types Mm which correspond to the so-called Bm Lie algebras. In this article we report on a simple model that suggests a mechanism by which standard odd-dimensional general relativity may emerge as the weak coupling constant limit of a (2p + 1)- dimensional Chern–Simons Lagrangian invariant under the Maxwell algebra type M2m+1, if and only if m ≥ p. Similarly, we show that standard even-dimensional general relativity emerges as the weak coupling constant limit of a (2p)- dimensional Born–Infeld type Lagrangian invariant under a subalgebra LM2m of the Maxwell algebra type, if and only if m ≥ p. It is shown that when m < p this is not possible for a (2p +1)-dimensional Chern–Simons Lagrangian invariant under the M2m+1 and for a (2p)-dimensional Born–Infeld type Lagrangian invariant under the LM2m algebra.

The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3, 2) leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D = 4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N ) recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N ). Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.