arXiv subjects

Eduardo Rodríguez

Publications and source records attributed to Eduardo Rodríguez.

21 records · Page 2Linked to original sources

arXiv2006

Expanding Lie (super)algebras through abelian semigroups

We propose an outgrowth of the expansion method introduced by de Azcarraga et al. [Nucl. Phys. B 662 (2003) 185]. The basic idea consists in considering the direct product between an abelian semigroup S and a Lie algebra g. General conditions under which relevant subalgebras can systematically be extracted from S \times g are given. We show how, for a particular choice of semigroup S, the known cases of expanded algebras can be reobtained, while new ones arise from different choices. Concrete examples, including the M algebra and a D'Auria-Fre-like Superalgebra, are considered. Finally, we find explicit, non-trace invariant tensors for these S-expanded algebras, which are essential ingredients in, e.g., the formulation of Supergravity theories in arbitrary space-time dimensions.

hep-th↗

arXiv2006

Transgression Forms and Abelian Semigroups in Supergravity

Two main themes populate this Thesis's pages: transgression forms as Lagrangians for gauge theories and the Abelian semigroup expansion of Lie algebras. A transgression form is a function of two gauge connections whose main property is its full invariance under gauge transformations. From this form a Lagrangian is built, and equations of motion, boundary conditions and associated Noether currents are derived. A subspace separation method, based on the extended Cartan homotopy formula, is proposed, which allows to (i) split the Lagrangian in 'bulk' and 'boundary' contributions and (ii) separate the bulk term in sublagrangians corresponding to the subspaces of the gauge algebra. Use is made of Abelian semigroups to develop an expansion method for Lie (super)algebras, based on the work by de Azcarraga, Izquierdo, Picon and Varela. The main idea consists in considering the direct product between an Abelian semigroup S and a Lie (super)algebra g. General conditions under which smaller algebras can be extracted from S \otimes g are given. It is shown how to recover the known expansion cases in this new context. Several d=11 superalgebras are obtained as examples of the application of the method. General theorems that allow to find an invariant tensor for the expanded algebra from an invariant tensor for the original algebra are formulated. Finally, a d=11 gauge theory for the M Algebra is considered by using the ideas developed in the Thesis. The dynamical properties of this theory are briefly analyzed.

hep-th↗

arXiv2006

On Transgression Forms and Chern--Simons (Super)gravity

A transgression form is proposed as lagrangian for a gauge field theory. The construction is first carried out for an arbitrary Lie Algebra g and then specialized to some particular cases. We exhibit the action, discuss its symmetries, write down the equations of motion and the boundary conditions that follow from it, and finally compute conserved charges. We also present a method, based on the iterative use of the Extended Cartan Homotopy Formula, which allows one to (i) systematically split the lagrangian in order to appropriately reflect the subspaces structure of the gauge algebra, and (ii) separate the lagrangian in bulk and boundary contributions. Chern--Simons Gravity and Supergravity are then used as examples to illustrate the method. In the end we discuss some further theoretical implications that arise naturally from the mathematical structure being considered.

hep-th↗