Zwei-Dreibein Gravity: A Two-Frame-Field Model of 3D Massive Gravity

Abstract

We present a generally covariant and parity-invariant two-frame field ("zwei-dreibein") action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.

Linearized gravity in terms of differential forms

“…The particular staggering of partial derivative indices in the expression (32) is reproduced by exterior algebra from the compact expression (29). It is worth to emphasize that the expression (32) is the expression obtained by making use of the linearized Christoffel symbols and the linearized Riemann tensor and that (32) is merely the expression of (29) in component form.…”

Anisotropic scale invariant spacetimes and black holes in Zwei-Dreibein Gravity

“…Very recently, a new 3D gravity model with very interesting properties, called ZweiDreibein Gravity (ZDG), was proposed [1]. It was shown in [18] that this bigravity theory can be viewed as a higher-derivative gravity theory of which NMG is a particular limit.…”

“…It was recently shown that this is the only asymptotatically Lifshitz black hole with z = 1 in the theory [23]. 1 The metric of this three-dimensional z = 3 Lifshitz black hole is given by the following line element…”

“…The remaining degree of freedom is potentially a ghost mode. One way to avoid this presumably ghost mode is by restricting the parameter space of the theory, for example, choosing β 2 = 0, and assuming that e 1 is invertible [1,[27][28][29]. 3 Therefore, the equations of motion for e 1 a , e 2 a , and ω I a , with β 2 = 0, and with an invertible e 1 , derived from the Lagrangian density (3.…”

“…[1]. ZDG is a bigravity theory whose dynamical fields are the two dreibein 1-forms e I a = e I µ a dx µ and the two spin-connection 1-forms ω I a = ω I µ a dx µ .…”