Dra. Rodríguez-Durán, Evelyn

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 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 a Born–Infeld gravity theory based on generalizations of Maxwell symmetries denoted as Cm. We analyze different configuration limits allowing to recover diverse Lovelock gravity actions in six dimensions. Further, the generalization to higher even dimensions is also considered.

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.