Abstract
The linearized equations of “New Massive Gravity” propagate a parity doublet of massive spin-2 modes in 3D Minkowski spacetime, but a different non-linear extension is made possible by “third-way” consistency. There is a “Chern-Simons-like” action, as for other 3D massive gravity models, but the new theory is “exotic”: its action is parity odd. This “Exotic Massive Gravity” is the next-to-simplest case in an infinite sequence of third-way consistent 3D gravity theories, the simplest being the “Minimal Massive Gravity” alternative to “Topologically Massive Gravity”.
Highlights
Omitting a possible cosmological constant term, the NMG field equation for the metric of a three-dimensional (3D) spacetime takes the form1
The simplest s = 2 example is the parity-violating Topologically Massive Gravity, or TMG, which is a 3rd-order extension of 3D General Relativity (GR) propagating a single massive spin-2 mode
If we insist on preservation of parity, which implies propagation of a parity doublet of massive spin-2 modes, the simplest example is “New Massive Gravity”, or NMG, which is a 4th-order extension of 3D GR
Summary
The new 3D massive gravity model that we have called “Exotic Massive Gravity” joins a very short list of field equations that are known to be third-way consistent; the only previously known examples, which are both in 3D, are “Minimal Massive Gravity” [22], which propagates a single spin-2 mode, and a modified 3D Yang-Mills equation that is related to multi-membrane dynamics [31]. If we add a multiple of Sμν to Eμν the first equality of (2.12) is still valid but when we use Eμν = 0 in the step we get an additional term because of the additional term in Eμν, but this additional term is proportional to ǫν ρσSρλSλσ This is identically zero for any symmetric S-tensor but this tensor will satisfy the Bianchi identity required for the validity of the first equality of (2.12) only if it is traceless, as it is for this EMG case. This special feature is what allows us to modify the EMG equation to get the EGMG equation of (1.8) without sacrificing consistency. An infinite number of third-way consistent field equations may be found in this way, but if we restrict to equations of 4th-order or less the only cases are MMG and EMG/EGMG
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