Dra. Rodríguez-Durán, Evelyn

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.

We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the bms3 algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the supertranslations in the standard bms3 algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions of standard asymptotically flat case. The field content of the theory is different than the one of General Relativity, but it includes all its geometries as particular solutions. In this line, we also study the stationary solutions of the theory in ADM form and we show that the vacuum energy and the vacuum angular momentum of the stationary configuration are influenced by the presence of the gravitational Maxwell field.

It is an accepted fact that requiring the Lovelock theory to have the maximum possible number of degree of freedom, fixes the parameters in terms of the gravitational and the cosmological constants. In odd dimensions, the Lagrangian is a Chern–Simons form for the (A)dS group. In even dimensions, the action has a Born–Infeld-like form. Recently was shown that standard odd-dimensional General Relativity can be obtained from Chern–Simons gravity theory for a certain Lie algebra B. Here we report on a simple model that suggests a mechanism by which standard even-dimensional General Relativity may emerge as a weak coupling constant limit of a Born–Infeld theory for a certain Lie subalgebra of the algebra B. Possible extension to the case of even-dimensional supergravity is briefly discussed.

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.

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.

We present a generalization of the standard Inönü–Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern–Simons supergravity action of a contracted superalgebra. In particular we show that the Poincaré limit can be performed to a D = 2 + 1 (p, q) AdS Chern–Simons supergravity in presence of the exotic form. We also construct a new three-dimensional(2, 0) Maxwell Chern–Simons supergravity theory as a particular limit of (2, 0) AdS–Lorentz supergravity theory. The generalization for N = p+q gravitinos is also considered.

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.

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.

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.

We present a generalization of the n-dimensional (pure) Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.