Comments on topologically massive gravity with propagating torsion

Abstract

We study and discuss some of the consequences of the inclusion of torsion in 3D Einstein-Chern-Simons gravity. Torsion may trigger the excitation of non-physical modes in the spectrum. Higher-derivative terms are then added up and tree-level unitarity is contemplated.

Remarks on Dirac-like monopoles, Maxwell and Maxwell-Chern-Simons electrodynamics inD=2+1dimensions

“…In this case, we cannot have bound states. 9 However, when the system is supplemented by an extra, say, scalar potential (as in the present case), it is also well-known that bound states show up, even in the case of repulsive potential [35]. Here, we have just raised such a question, and a precise answer demands further investigation.…”

Discussing quantum aspects of higher-derivative 3-D gravity in the first-order formalism

“…λ e ξ are the gauge-fixing parameters. The wave operator, M , can be expressed in terms of an extension of the spin-projection operator formalism introduced in [29], [30,31,13].…”

“…Motivated by these these recent results, we propose here to pursue an investigation of planar gravity actions with propagating tensor, since we have in mind to understand which role torsion degrees of freedom may play in connection with unitary higher-derivative gravitation in 3D. In order to investigate this further, we begin with the analysis of a traditional (1+2)-D gravity model previously done by two of us [13], where we have studied the inclusion of torsion in three-dimensional Einstein-Chern-Simons gravity and added up higher-derivative terms; we have worked in affine connection formalism. In this work, due to invertibility problems that appear in the theory if we adopt the first-order approach, we are lead to change to another Lagrangian density, where we introduce torsion algebraic terms, yielding dynamical spin-connection.…”

Propagating torsion in 3D gravity and dynamical mass generation

“…As we shall soon understand, only the ϕ-component indeed minimally couples to fermions. On the other hand, it is worthwhile to mention that the spin-2 component, X µν , plays a peculiar role when Chern-Simons gravity is considered: it influences the spin-2 sector of the graviton propagator and it is responsible for the appearance of a massive ghost-like mode in the spectrum [5].…”

“…Having in mind that topologically massive 3D gravity with dynamical torsion exhibits a number of peculiar results [5,6], we propose here to pursue the investigation of dynamical mass generation for fermionic matter and a 2-form gauge potential that interact with gravitational field whose torsion fluctuations dominate over the metric excitations. In practice, this means that we adopt 3D space-time as a flat background on which the torsion degrees of freedom propagate and interact with matter and gauge fields -it might corresponds to a physical situation where the torsion field is produced by a cosmological neutrino sea [7].…”