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

Barnich, Glenn; Compère, Geoffrey

doi:10.1088/0264-9381/24/5/f01

Cited by 304 publications

(478 citation statements)

References 36 publications

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“…Such GR 3 and CS + matter theories are well-known to have infinite-dimensional AS [57][58][59][60][61][62][63][64][65] in section 2). The infinity of (AS) charges of CFT 2 (AdS 3 ) form a well-known type of 2D (3D) "hair", operating on and finely diagnosing quantum states, in a manner generalizing the action of ordinary conserved global charges.…”

Section: Jhep01(2018)014mentioning

confidence: 99%

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Asymptotic symmetries, holography and topological hair

Mishra¹,

Sundrum²

2018

J. High Energ. Phys.

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Asymptotic symmetries of AdS 4 quantum gravity and gauge theory are derived by coupling the holographically dual CFT 3 to Chern-Simons gauge theory and 3D gravity in a "probe" (large-level) limit. Despite the fact that the three-dimensional AdS 4 boundary as a whole is consistent with only finite-dimensional asymptotic symmetries, given by AdS isometries, infinite-dimensional symmetries are shown to arise in circumstances where one is restricted to boundary subspaces with effectively two-dimensional geometry. A canonical example of such a restriction occurs within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS 4 quantum gravity. An AdS 4 analog of Minkowski "super-rotation" asymptotic symmetry is probed by 3D Einstein gravity, yielding CFT 2 structure (in a large central charge limit), via AdS 3 foliation of AdS 4 and the AdS 3 /CFT 2 correspondence. The maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D gravities have Chern-Simons formulation, manifesting their topological character. Chern-Simons structure is also shown to be emergent in the Poincare patch of AdS 4 , as soft/boundary limits of 4D gauge theory, rather than "put in by hand" as an external probe. This results in a finite effective Chern-Simons level. Several of the considerations of asymptotic symmetry structure are found to be simpler for AdS 4 than for Mink 4 , such as non-zero 4D particle masses, 4D non-perturbative "hard" effects, and consistency with unitarity. The last of these in particular is greatly simplified because in some setups the time dimension is explicitly shared by each level of description: Lorentzian AdS 4 , CFT 3 and CFT 2 . Relatedly, the CFT 2 structure clarifies the sense in which the infinite asymptotic charges constitute a useful form of "hair" for black holes and other complex 4D states. An AdS 4 analog of Minkowski "memory" effects is derived, but with late-time memory of earlier events being replaced by (holographic) "shadow" effects. Lessons from AdS 4 provide hints for better understanding Minkowski asymptotic symmetries, the 3D structure of its soft limits, and Minkowski holography.

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Section: Jhep01(2018)014mentioning

confidence: 99%

“…This AS of Mink 3 is XBMS 3 [58]. Here we review its derivation by a "contraction" of the Vir + × Vir − AS of AdS 3 , essentially getting flat 3D by taking the R AdS 3 → ∞ limit [59,[76][77][78][79][80][81].…”

Section: Non-unitary Nature Of Cgrmentioning

confidence: 99%

Asymptotic symmetries, holography and topological hair

Mishra¹,

Sundrum²

2018

J. High Energ. Phys.

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“…This was based on the fact that the asymptotic symmetry group (ASG) of asymptotically flat spacetimes at null infinity is the Bondi, van der Burg, Metzner and Sachs (BMS) group [4][5][6]. In three and four dimensions, BMS group is infinite dimensional and the corresponding algebra can be centrally extended [7]- [9]. Thus it is probable that the theory dual to three or four dimensional flat space is given by a (two or three dimensional) field theory living on its null boundary which has exactly the symmetries of the BMS group.…”

Section: Introductionmentioning

confidence: 99%

Flat-space energy-momentum tensor from BMS/GCA correspondence

Fareghbal

Naseh

2014

J. High Energ. Phys.

100

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Flat-space limit is well-defined for asymptotically AdS spacetimes written in coordinates called the BMS gauge. For the three-dimensional Einstein gravity with a negative cosmological constant, we calculate the quasi-local energy momentum tensor in the BMS gauge and take its flat-space limit. In defining the flat-space limit, we use the BMS/GCA correspondence which is a duality between gravity in flat-spacetime and a field theory with Galilean conformal symmetry. The resulting stress tensor reproduces correct values for conserved charges of three dimensional asymptotically flat solutions. We show that the conservation relation of the flat-space energy-momentum tensor is given by an ultra-relativistic contraction of its relativistic counterpart. The conservation equations correspond to Einstein equation for the flat metric written in the BMS gauge. Our results provide further checks for the proposal that the holographic dual of asymptotically flat spacetimes is a field theory with Galilean conformal symmetry.

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“…In pure Einstein gravity in three dimensions, it was observed that the asymptotic algebra picks up central extensions [8]. It turns out that the BMS 3 algebra [7] is related to the conformal algebra through a redefinition of generators and taking the cosmological constant to zero [8][9][10].…”

mentioning

confidence: 99%

“…We impose boundary conditions on the metric g µν , which generalize/correct the ones proposed in [8]:…”

mentioning

confidence: 99%

Flat-Space Chiral Gravity

2012

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We provide the first evidence for a holographic correspondence between a gravitational theory in flat space and a specific unitary field theory in one dimension lower. The gravitational theory is a flat-space limit of topologically massive gravity in three dimensions at Chern-Simons level k=1. The field theory is a chiral two-dimensional conformal field theory with central charge c=24.Comment: 5 pages, v2: minor rearrangement

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

Cited by 304 publications

References 36 publications

Asymptotic symmetries, holography and topological hair

Asymptotic symmetries, holography and topological hair

Flat-space energy-momentum tensor from BMS/GCA correspondence

Flat-Space Chiral Gravity

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