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.

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 = 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 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.

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.