Dra. Rodríguez-Durán, Evelyn

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.

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 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.