Aspects of the BMS/CFT correspondence

Abstract

ABSTRACT. After a review of symmetries and classical solutions involved in the AdS 3 /CFT 2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi's news tensor, mass and angular momentum aspects under local conformal transformations.

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

“…This result again coincides with direct calculations of [9]. Using (2.14), one can find asymptotic symmetry group of flat spacetimes.…”

“…σ ab dx a dx b = G 2 dφ 2 and v µ is the unit timelike vector normal to Σ. Putting every things together we find 19) which is consistent with the result of [9].…”

“…The line element (2.13) with condition (2.12) is exactly the generic result which one may find for solutions of Einstein gravity (without cosmological constant) in the BMS gauge (2.2) [9]. We should emphasize that we don't use the modified Penrose limit of [20] which needs the scaling of the Newton constant G and results in an ambiguity in the definition of conserved charges.…”

“…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.…”

Flat-Space Chiral Gravity

“…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]. Also, the general asymptotically flat solution to Einstein gravity could be obtained as a limit of the general solution in AdS 3 [11,12]. From the field theory point of view, it was shown that the limit of large AdS radius is perceived as a contraction on the dual CFT [9,10].…”