arXiv subjects
Publications and source records attributed to J. E. Rosales-Quintero.
Starting with the MacDowell-Mansouri formulation of gravity with a $SO(4,1)$ gauge group, we introduce new parameters into the action to include the non-dynamical Holst term, and the topological Nieh-Yan and Pontryagin classes. Then, we consider the new parameters as fields and analyze the solutions coming from their equations of motion. The new fields introduce torsional contributions to the theory that modify Einstein's equations.
In this work we study the symmetry breaking conditions, given by a (anti)de Sitter-valued vector field, of a full (anti)de Sitter-invariant MacDowell-Mansouri inspired action. We show that under these conditions the action breaks down to General Relativity with a cosmological constant, the four dimensional topological invariants, as well as the Holst term. We obtain the equations of motion of this action, and analyze the symmetry breaking conditions.
We study an $SO(1,3)$ pure connection formulation in four dimensions for real-valued fields, inspired by the Capovilla, Dell and Jacobson complex self-dual approach. By considering the CMPR BF action, also, taking into account a more general class of the Cartan-Killing form for the Lie algebra $\mathfrak{so(1,3)}$ and by refining the structure of the Lagrange multipliers, we integrate out the metric variables in order to obtain the pure connection action. Once we have obtained this action, we impose certain restrictions on the Lagrange multipliers, in such a way that the equations of motion led us to a family of torsionless conformally flat Einstein manifolds, parametrized by two numbers. Finally, we show that, by a suitable choice of parameters, that self-dual spaces (Anti-) De Sitter can be obtained.
We introduce a complex pure connection action with constraints which is diffeomorphism and gauge invariant. Taking as an internal group $SU(2)$, we obtain, from the equations of motion, anti-self-dual Einstein spaces together with the zero torsion condition thanks to Bianchi identity. By applying the same procedure, we take as internal symmetry the super group $OSp(1|2)$ and by means of the Bianchi identity and integrability conditions, the equations of motion are those that come from anti-self-dual supergravity $N=1$ with cosmological constant sector.
We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space-time diffeomorphisms, which at the action level, corresponds to the Kalb-Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.