Generalized Pure Lovelock Gravity

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.Comment: v2, 16 pages, references and comments adde

Geometrical Formulation of Supergravity Theories

This thesis deals with a geometrical formulation of diverse Supergravity theories. In particular, the construction of Supergravity actions in four and three dimensions are considered in dierent frameworks with interesting physical implications. Before approaching supersymmetry, we brie y review some gravity theories in the Cartan formalism. The formalism used in the introductory chapter is crucial in order to understand the development of the present thesis. Some interesting results are presented in chapter 2 using the semigroup expansion method in the Chern-Simons (CS) and Born-Infeld (BI) gravity theories. Subsequently, a brief introduction of supersymmetry and some supergravity models are considered in chapter 3. Chapters 4, 5, 6 and 7 contain the main results of this thesis which are based on ve articles written during the cotutelle research process. Initially, we present a family of superalgebras using the semigroup expansion of the Anti-de Sitter superalgebra. In the MacDowell-Mansouri approach, we study the construction of diverse four-dimensional supergravity theories for dierent superalgebras. Interestingly, we show that the pure supergravity action can be obtained as a MacDowell-Mansouri like action using the Maxwell symmetries. Additionally, a generalized supersymmetric cosmological constant term can be included to a supergravity theory using a particular supersymmetry, called AdS-Lorentz. Furthermore, we present a supergravity model in three dimensions using the CS formalism and the Maxwell superalgebras. Subsequently, the thesis is focused on a supergravity model with partial breaking of N = 2 to N = 1 supersymmetry which, in the low energy limit, gives rise to a N = 1 supersymmetric theory. Eventually, the thesis ends with some comments about possible developments

Generalized Chern-Simons higher-spin gravity theories in three dimensions

The coupling of spin-3 gauge fields to three-dimensional Maxwell and $AdS$-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the $AdS$ and the Poincar\'e algebras in three dimensions can be obtained as expansions of $\mathfrak{sl}\left( 3,\mathbb{R}\right)$ algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higher-spin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the $AdS$-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein gravity.Comment: version 3, 28 pages, accepted version in Nuclear Physics

Three-dimensional non-relativistic supergravity and torsion

In this paper we present a torsional non-relativistic Chern-Simons teleparallel (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of the purely bosonic relativistic teleparallel Chern-Simons formulation of gravity. On-shell the latter yields a non-Riemannian setup with non-vanishing torsion, which, at non-relativistic level, translates into a non-vanishing spatial torsion sourced by the cosmological constant. Then we consider the three-dimensional relativistic $\mathcal{N}=2$ Chern-Simons supergravity theory and obtain its non-relativistic counterpart by exploiting a Lie algebra expansion method. The non-relativistic supergravity theory is characterized, on-shell, by a non-vanishing spatial super-torsion, again sourced by the cosmological constant.Comment: 23 page

Non-relativistic limit of the Mielke-Baekler gravity theory

In this paper, we present the most general non-relativistic Chern-Simons gravity model in three spacetime dimensions. We first study the non-relativistic limit of the Mielke-Baekler gravity through a contraction process. The resulting non-relativistic theory contains a source for the spatial component of the torsion and the curvature measured in terms of two parameters, denoted by $p$ and $q$. We then extend our results by defining a Newtonian version of the Mielke-Baekler gravity theory, based on a Newtonian like algebra which is obtained from the non-relativistic limit of an enhanced and enlarged relativistic algebra. Remarkably, in both cases, different known non-relativistic and Newtonian gravity theories can be derived by fixing the $\left(p,q\right)$ parameters. In particular, torsionless models are recovered for $q=0$.Comment: 20 page

On the supersymmetry invariance of flat supergravity with boundary

The supersymmetry invariance of flat supergravity (i.e., supergravity in the absence of any internal scale in the Lagrangian) in four dimensions on a manifold with non-trivial boundary is explored. Using a geometric approach we find that the supersymmetry invariance of the Lagrangian requires to add appropriate boundary terms. This is achieved by considering additional gauge fields to the boundary without modifying the bulk Lagrangian. We also construct an enlarged supergravity model from which, in the vanishing cosmological constant limit, flat supergravity with a non-trivial boundary emerges properly.Comment: V2, 26 pages, discussions, motivation and references adde