The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA, obtained from a linear combination of two copies of the Virasoro algebra, is generically non-unitary. The unitary subsector previously constructed had trivial correlation functions. We consider a representation obtained from a different linear combination of the Virasoros, which is relevant to the relation with the BMS algebra in three dimensions. This is realised by a new space-time contraction of the parent algebra. We show that this representation has a unitary sub-sector with interesting correlation functions. We discuss implications for the BMS/GCA correspondence and show that the flat space limit actually induces precisely this contraction on the boundary conformal field theory. We also discuss aspects of asymptotic symmetries and the consequences of this contraction in higher dimensions. arXiv:1203.5795v2 [hep-th]

We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R 1,2 , the flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry non-zero charges under the asymptotic symmetry algebra of R 1,2 , the 3d Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the 2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro algebra, which is isomorphic to BMS3. We study flat holography as a limit of AdS3/CFT2 to semi-classically compute the density of states in the dual, exactly reproducing the bulk entropy in the limit of large charges. Our flat horizons, remnants of the BTZ inner horizons also satisfy a first law of thermodynamics. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers.

We present the first example of a nontrivial higher spin theory in three-dimensional flat space. We propose flat-space boundary conditions and prove their consistency for this theory. We find that the asymptotic symmetry algebra is a (centrally extended) higher spin generalization of the Bondi-Metzner-Sachs algebra, which we describe in detail. We also address higher spin analogues of flat space cosmology solutions and possible generalizations.

We study Einstein gravity in dimensions D ≥ 4 modified by curvature squared at critical point where the theory contains only massless gravitons. We show that at the critical point a new mode appears leading to a logarithmic gravity in the theory. The corresponding logarithmic solution may provide a gravity description of logarithmic CFT in higher dimensions. We note also that for special values of the parameters of the theory, the model admits solutions with non-relativistic isometries.