The third way to 3D gravity

Bergshoeff, Eric; Merbis, Wout; Routh, Alasdair J.; Townsend, Paul

doi:10.1142/s0218271815440150

Cited by 30 publications

(26 citation statements)

References 19 publications

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“…It generalizes topologically massive gravity theory (TMG) [4] supplementing it with third-and fourth-order terms. EMG can be regarded as the next-tosimplest example of an infinite sequence of consistent 3D models obeying what has been called the third-way mechanism [5], i.e. a mechanism by means of which classical metric theories with no action can still satisfy the Bianchi identities on-shell without imposing additional constraints.…”

Section: Introductionmentioning

confidence: 99%

More on vacua of exotic massive 3D gravity

Giribet

Oliva

2019

Phys. Rev. D

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In a recent paper [1], we explored the space of solutions of the exotic massive 3D gravity theory proposed in [2]. We showed that the theory admits a rich space of vacua, including asymptotically Anti de-Sitter (AdS) geometries obeying different types of boundary conditions. The examples include black holes dressed with low decaying gravitons. Based on what happens in other theories of massive gravity, we conjectured that such geometries appear on a curve of the parameter space (chiral curve) where the exotic massive gravity on AdS with sufficiently strong boundary conditions results dual to a 2D chiral conformal field theory. Here, we show that this expectation is consistent with the conserved charges and thermodynamical properties of the black holes of the theory, which have recently been computed [3]. When the boundary conditions are relaxed relative to the standard Brown-Henneaux boundary conditions, the theory exhibits solutions consistent with the definition of the so-called Log-gravity. The asymptotic behavior of these solutions presents a logarithmic term in the Fefferman-Graham expansion that, nonetheless, is compatible with the AdS asymptotic symmetries. This long range interaction is due to a mode of the massive gravity that becomes massless precisely on the chiral curve.We construct exact solutions exhibiting this behavior, which admit to be interpreted as fully backreacting gravitational waves propagating on an extremal black hole, and carrying nonvanishing gravitational energy. We also discuss other vacua of the theory, such as Warped-AdS 3 black holes, gravitational waves on such backgrounds, AdS 2 × S 1 spaces, and black holes in dS 3 space.

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Section: Introductionmentioning

confidence: 99%

More on vacua of exotic massive 3D gravity

Giribet

Oliva

2019

Phys. Rev. D

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“…Recently, two situations defying the rigidity of Einstein gravity were actively explored. One is the massive modification of gravity [7][8][9][10], along with numerous variants in three dimensions [11,12]. Another is higher-derivative modifications of the gravity [13,14].…”

Section: Introductionmentioning

confidence: 99%

Rainbow valley of colored (anti) de Sitter gravity in three dimensions

Gwak

Joung

Mkrtchyan

et al. 2016

J. High Energ. Phys.

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We propose a theory of three-dimensional (anti) de Sitter gravity carrying Chan-Paton color charges. We define the theory by Chern-Simons formulation with the gauge algebra (gl 2 ⊕ gl 2 ) ⊗ u(N ), obtaining a color-decorated version of interacting spinone and spin-two fields. We also describe the theory in metric formulation and show that, among N 2 massless spin-two fields, only the singlet one plays the role of metric graviton whereas the rest behave as colored spinning matter that strongly interacts at large N . Remarkably, these colored spinning matter acts as Higgs field and generates a non-trivial potential of staircase shape. At each extremum labelled by k = 0, . . . , [ N −1 2 ], the u(N ) color gauge symmetry is spontaneously broken down to u(N − k) ⊕ u(k) and provides different (A)dS backgrounds with the cosmological constants N N −2k 2 Λ. When this symmetry breaking takes place, the spin-two Goldstone modes combine with (or are eaten by) the spin-one gauge fields to become partially-massless spin-two fields. We discuss various aspects of this theory and highlight physical implications.

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“…This condition does however not follow from the above definition (3.8) of the tensor L µν , which means as expected that these equations of motion cannot be derived from a purely metric action. Instead, consistency is achieved via the so-called "third way" of [17], i.e. using the equations of motion themselves.…”

Section: )mentioning

confidence: 99%

Metric formulation of the simple theory of 3d massive gravity

Geiller

Noui

2019

Phys. Rev. D

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We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal Lorentz gauge symmetry is broken. The absence of Lorentz invariance, which in this model is the mechanism underlying the propagation of a massive graviton, does however prevent from writing a purely metric non-linear action for the theory. Nonetheless, in this letter, we explain how to disentangle, at the non-linear level, the metric and non-metric degrees of freedom in the equations of motion. Focusing on the metric part, we show that it satisfies modified Einstein equations with higher derivative terms. As a particular case, these equations reproduce a well-studied model known as minimal massive gravity. In the general case, we obtain new metric field equations for massive gravity in three dimensions starting from the simple first order action. These field equations are consistent through a mechanism known as "third way consistency", which our theory therefore provides a new example of.

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The third way to 3D gravity

Cited by 30 publications

References 19 publications

More on vacua of exotic massive 3D gravity

More on vacua of exotic massive 3D gravity

Rainbow valley of colored (anti) de Sitter gravity in three dimensions

Metric formulation of the simple theory of 3d massive gravity

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