Chern-Simons gravity with(curvature)2and(torsion)2

Abstract

We investigate the effects of (Curvature) 2 -and (Torsion) 2 -terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum. * Electronic address: helayel@cbpf.br † Electronic address: carlos@cbpf.br ‡ Electronic address: bpdias@cbpf.br § Electronic address: alfredov@cbpf.br ¶ Electronic address: vjose@cbpf.br

Probing the effects of Lorentz-symmetry violating Chern-Simons and Ricci-Cotton terms in higher derivative gravity

“…There is indeed a great resemblance between massive particles in 3D and massless particles in 4D, since they essentially share the same representation structure of the Poincaré group. As in 3D, parity-breaking terms yield different masses for particles that would propagate as doublet of spins, as discussed in [26]. This same role of the parity-breaking shows up in the massless graviton propagator (37), where the helicities modes are no more related by CPT transformations.…”

“…On the other hand, in a paritybreaking theory, such as gravity theories added to a Chern-Simons parity-breaking term, this doublet structure is lost and each spin component acquires a different mass, which we interpret as degrees of freedom propagating independently. For more details, see [26].…”

“…In order to fulfill the task of analyzing the spectral properties of these modified gravities, we follow the lines of previous works [24][25][26] and build up an orthonormal basis of operators that splits the fundamental fields into their individual degrees of freedom. With this basis, the attainment of the propagator is feasible and it is possible to identify the excitation modes of the model.…”

Vaidya-like exact solutions with torsion

“…The boundary terms for ξ t = 1 and ξ ϕ = 1, 8) represent the energy and angular momentum of the system, respectively. Calculated on the Vaidya-OTT configuration, these expressions take the values…”

“…However, this model is, just like GR, a topological theory without propagating degrees of freedom. In PGT, such an unrealistic dynamical feature can be quite naturally improved by going over to Lagrangians that are quadratic in the field strengths [8,9], as in the standard gauge theories.…”