|3-Dimensional Massive Gravity Theories|
In General > s.a. 3D gravity theories.
* Idea: Theories obtained by adding to Einstein's gravity the usual Fierz-Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary, but have their unitarity spoiled when a Chern-Simons term is added (topologically massive).
@ General references: Bañados & Theisen JHEP(09) [as bimetric gravity, and black holes]; Grigore & Scharf a1008; Sadegh & Shirzad PRD(11)-a1010 [constraint structure]; Zinoviev CQG(13)-a1205 [and bigravity]; Hohm et al PRD(12)-a1208 [Chern-Simons-like action, and Hamiltonian]; Edelstein et al PRD(17)-a1602 [causality].
@ Black holes: Ayón-Beato et al PRD(09) [Lifshitz metrics]; Tonni JHEP(10)-a1006 [warped black holes]; Ghodsi & Moghadassi PLB(11)-a1007, Flory & Sachs PRD(13)-a1304, Kwon et al JHEP(13)-a1308 [new massive gravity].
Topologically Massive Gravity
> s.a. 3D quantum gravity; bel-robinson tensor;
Faddeev-Jackiw Method; massive gravity.
* Idea: Three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term.
* Action: The Einstein action (≅ ISO(2,1) Chern-Simons) plus a conformal gravity term (≅ SO(2,1)-Chern-Simons or SO(3)-Chern-Simons).
* Field equations: If m is the topological coupling constant, and C the (traceless) Cotton tensor, then
Gab + m−1 Cab = −k Tab ;
Notice that, since Cab contains
derivatives of Rab, the field
equations are third-order; It propagates a single massive spin-2 graviton mode.
* Drawback: One of the two (left/right) central charges of the corresponding putative boundary cft can be shown to be negative whenever the bulk AdS graviton has positive energy, which is inconsistent with quantum unitarity.
@ General references: Peldán CQG(92); Deser et al NPB(94)ht/93 [particle scattering amplitudes]; Accioly & Dias IJMPA(06)ht/05 [non-unitarity]; Grumiller & Jackiw a0802-wd [with Λ < 0, and complex Chern-Simons terms]; Grumiller et al a0806-in [cosmological, at the chiral point]; Carlip et al PLB(08)-a0807, Carlip JHEP(08)-a0807 [in AdS spacetime, constraint algebra]; Giribet et al JHEP(08)-a0807 [and chirality]; Grumiller & Johansson JHEP(08) [chiral point instability]; Oda a0905 [renormalizability]; Lashkari & Maloney CQG(11)-a1007 [and Ricci-Cotton Flow]; Grumiller & Vassilevich JHEP(10)-a1007 [graviton 1-loop partition function]; > s.a. energy positivity.
@ Canonical formulation: Hotta et al JHEP(08)-a0805 [Brown-Henneaux approach]; Blagojević & Cvetković JHEP(09)-a0812 [with cosmological constant]; Mišković & Olea JHEP(09)-a0909 [background-independent charges]; > s.a. symplectic structures.
@ Black holes: Dereli & Sarioglu gq/00; Birmingham et al PRD(10)-a1006 [BTZ black hole, stability]; Flory & Sachs PRD(13)-a1304 [non-stationary exact solution]; Troessaert et al a1512-ln [and gravitational waves]; > s.a. black-hole perturbations.
@ Other solutions: Nutku & Baekler AP(89) [homogeneous, anisotropic]; Clément CQG(90) [point sources]; Ortiz AP(90) [homogeneous], CQG(90) [spinning sources]; Edery & Paranjape PLB(97), PLB(97)gq [localized mass and spin]; Dereli & Sarioglu PLB(00)gq [+ Maxwell-Chern-Simons, self-dual]; Henneaux et al PRD(09)-a0901 [asymptotically AdS spacetimes]; Chow et al CQG(10)-a0906 [classification]; Ertl et al CQG(10)-a1006 [stationary axisymmetric]; Henneaux et al PRD(11)-a1108 [asymptotically warped AdS spacetimes]; Moon & Myung PRD(12)-a1111 [polarization modes of gravitational waves]; > s.a. anti-de sitter spacetime; Kundt Spacetimes.
Quantum Theory > s.a. 3D quantum gravity.
@ Topologically massive gravity: Deser & Yang CQG(90) [1-loop renormalizability]; Castro et al JHEP(11)-a1105 [with positive cosmological constant].
Other Theories > s.a. 3D gravity theories [massive 3D supergravity].
* Minimal massive gravity: A theory that may be considered a variation on topologically massive gravity, and also propagates a single massive spin-2 graviton mode, but in which the field equations are not the Euler-Lagrange equations of any action constructed only from the metric, and are nevertheless consistent; Both central charges of the dual cft are positive, and it also seems possible to consistently couple matter.
* Other variants of topologically massive gravity: Various higher-derivative modifications have been proposed to circumvent the negative-central-charge problem but, except for Minimal Massive Gravity they have always introduced additional, unphysical degrees of freedom.
@ Minimal massive 3D gravity: Bergshoeff et al CQG(14)-a1404 and CQG+; Tekin PRD(14)-a1409 [excitations and conserved charges]; Alishahiha et al JHEP(14)-a1409; Setare NPB(15)-a1412 [in 3D AdS background]; Yekta PRD(15)-a1503 [Hamiltonian formalism].
@ Variants of topologically massive gravity: Chen et al PLB(11)-a1106, Bagchi et al JHEP(11)-a1107 [spin-3]; Chen & Long JHEP(11); > s.a. dirac fields in curved spacetimes; supergravity.
@ Other theories: Bergshoeff et al PRL(09)-a0901 [higher-order theory, and massive Pauli-Fierz]; Paulos PRD(10)-a1005 [with curvature corrections]; Afshar et al JHEP(14)-a1405 [extended]; Geiller & Noui a1812 [simple theory, triad variables].
– journals – comments
– other sites – acknowledgements
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