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C. E. Valcárcel

Publications and source records attributed to C. E. Valcárcel.

9 recordsLinked to original sources
arXiv2020

Spin-3 fields in Mielke-Baekler gravity

Mielke-Baekler gravity consists in the usual Einstein-Hilbert action with a cosmological term and rotational and translational Chern-Simons terms with arbitrary couplings. For a particular choice of these couplings, we can obtain Einstein-Hilbert action, its teleparallel equivalent, and the exotic Witten's gravity. In this work, we use the Chern-Simons formalism to generalize the three dimensional Mielke-Baekler gravity theory in order to introduce spin-3 fields. We study its asymptotic symmetries, black hole solution, and also analyse its canonical structure at its singular point.

hep-th↗
arXiv2019

New boundary conditions for (extended) $\mathrm{AdS}_3$ supergravity

In this work, we build the most general boundary conditions for $\mathcal N=\left(1,1\right)$ and $\mathcal N=\left(2,2\right)$ extended supergravity. We show that for the loosest set of boundary conditions, their asymptotic symmetry algebras are two copies of the $\mathfrak{osp}\left(1\mid 2\right)_k$ and $\mathfrak{osp}\left(2\mid 2\right)_k$ algebra, respectively. Then, we restrict the gauge fields on the boundary conditions in order to obtain supersymmetric extensions of the Brown-Henneaux and Troessaert boundary conditions. Furthermore, for $\mathcal N=1$ and $\mathcal N=2$ (extended) supergravity we show the supersymmetric extensions of Avery-Poojary-Suryanarayana boundary conditions.

hep-th↗
arXiv2017

Hamilton-Jacobi analysis of the four dimensional BF model with cosmological term

In this work we perform the Hamilton-Jacobi constraint analysis of the four dimensional Background Field (BF) model with cosmological term. We obtain the complete set of involutive Hamiltonians that guarantee the integrability of the system and identify the reduced phase space. From the fundamental differential we recover the equations of motion and obtain the generators of the gauge and shift transformations.

hep-th↗
arXiv2016

Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory

Quadratic gravity in two dimensions can be formulated as a Background Field (BF) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions. In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.

hep-th↗
arXiv2015

Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis

We analyse the constraint structure of the Background Field model for three dimensional gravity including a cosmological term via the Hamilton-Jacobi formalism. We find the complete set of involutive Hamiltonians that assures the integrability of the system and calculate the characteristic equations of the system. We established the equivalence between these equations and the field equations and also obtain the generators of canonical and gauge transformations.

hep-th↗
arXiv2014

Involutive constrained systems and Hamilton-Jacobi formalism

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems.

hep-th↗
arXiv2011

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.

gr-qc↗
arXiv2008

Non-Involutive Constrained Systems and Hamilton-Jacobi Formalism

In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the integrability conditions leads to the reduction of degrees of freedom of these systems and, as consequence, naturally defines a dynamics in a reduced phase space.

hep-th↗