Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

Barnich, Glenn; Compère, Geoffrey

doi:10.1088/0264-9381/24/11/c01

Cited by 202 publications

(365 citation statements)

References 25 publications

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“…and hence, by virtue of (15), the global charges (44) reduce to the ones of the asymptotically flat case given in (18).…”

Section: B Vanishing Cosmological Constant Limitmentioning

confidence: 99%

“…A similarly rich asymptotic structure for flat three-dimensional gravity can be defined at null infinity [17][18][19] and is connected through a well-defined flat-space limit to the one of AdS 3 [20][21][22][23][24][25]. In particular, the limit of BTZ black holes are cosmologies [26,27] whose horizon entropy can be understood from symmetry arguments [28,29] consistent with those of the AdS 3 case [30], while the boundary dynamics [31] is a flat limit of Liouville theory [32], obtained through a Hamiltonian reduction from a chiral ISO(2, 1) Wess-Zumino-Witten theory [33,34].…”

Section: Introductionmentioning

confidence: 96%

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Asymptotic symmetries and dynamics of three-dimensional flat supergravity

Barnich

Donnay

Matulich

et al. 2014

J. High Energ. Phys.

103

153

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A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS3 algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS3 supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS3 algebra with an additional central charge.

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“…and hence, by virtue of (15), the global charges (44) reduce to the ones of the asymptotically flat case given in (18).…”

Section: B Vanishing Cosmological Constant Limitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Asymptotic symmetries and dynamics of three-dimensional flat supergravity

Barnich

Donnay

Matulich

et al. 2014

J. High Energ. Phys.

103

153

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“…One may also wonder about whether the asymptotically locally flat black hole (70), and the gravitational soliton (71) can be accommodated within a suitable set of asymptotic conditions at null infinity, along the lines of Ref. [54].…”

Section: Vanishing Cosmological Constantmentioning

confidence: 99%

Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

Oliva

Tempo

Troncoso

2009

J. High Energy Phys.

158

266

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The theory of massive gravity in three dimensions recently proposed by Bergshoeff, Hohm and Townsend (BHT) is considered. At the special case when the theory admits a unique maximally symmetric solution, a conformally flat solution that contains black holes and gravitational solitons for any value of the cosmological constant is found. For negative cosmological constant, the black hole is characterized in terms of the mass and the "gravitational hair" parameter, providing a lower bound for the mass. For negative mass parameter, the black hole acquires an inner horizon, and the entropy vanishes at the extremal case. Gravitational solitons and kinks, being regular everywhere, can be obtained from a double Wick rotation of the black hole. A wormhole solution in vacuum that interpolates between two static universes of negative spatial curvature is obtained as a limiting case of the gravitational soliton with a suitable identification. The black hole and the gravitational soliton fit within a set of relaxed asymptotically AdS conditions as compared with the one of Brown and Henneaux. In the case of positive cosmological constant the black hole possesses an event and a cosmological horizon, whose mass is bounded from above. Remarkably, the temperatures of the event and the cosmological horizons coincide, and at the extremal case one obtains the analogue of the Nariai solution, dS 2 × S 1 . A gravitational soliton is also obtained through a double Wick rotation of the black hole. The Euclidean continuation of these solutions describes instantons with vanishing Euclidean action. For vanishing cosmological constant the black hole and the gravitational soliton are asymptotically locally flat spacetimes. The rotating solutions can be obtained by boosting the previous ones in the t − φ plane.

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“…The generator J arises naturally when one derives the generators of the ECGA from a contraction of a pair conformal algebras with non-vanishing spin [39], whereas the choice R has a fairly natural form, especially in the auxiliary variables ν. Both generators obey the same commutators (8) with the other generators of ECGA and commute with the Schrödinger operator (9). One speaks of 'J-invariance' if the generator J is used and of 'R-invariance', if the generator R is used.…”

Section: Exotic Conformal Galilean Algebramentioning

confidence: 99%

“…In the context of asymptotically flat 3D gravity, an isomorphic Lie algebra is known as BMS algebra, bms 3 ≡ CGA(1)[8,9,6,7].…”

mentioning

confidence: 99%

Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

Henkel

Stoimenov

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Indecomposable but reducible representations of several Lie algebras of local scale-transformations, including the Schrödinger and conformal Galilean algebras, and their applications in physical ageing are reviewed. The physical requirement of the decay of co-variant two-point functions for large distances is related to analyticity properties in the coordinates dual to the physical masses or rapidities.

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Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

Abstract: The PDF file provided contains the full details of the corrigendum.

Cited by 202 publications

References 25 publications

Asymptotic symmetries and dynamics of three-dimensional flat supergravity

Asymptotic symmetries and dynamics of three-dimensional flat supergravity

Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity

Physical Ageing and New Representations of Some Lie Algebras of Local Scale-Invariance

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