Holography of 3D Flat Cosmological Horizons

Abstract

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.

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

“…It was shown in [14] that a Cardy-like formula for field theories with Galilean conformal symmetry in two dimensions (resulting from time-contraction of two dimensional CFT on the cylinder) produces the same entropy as that of three-dimensional cosmological solutions of flat gravity. These solutions of Einstein gravity in three dimensions were first studied in [15] and are shiftboost orbifolds of three dimensional Minkowski spacetime.…”

“…2 It was shown in [14] that (3.1) gives the correct entropy for the cosmological horizon of the three dimensional Einstein gravity solution which is the flat limit of BTZ black holes. This is an evidence in favour of the correctness of BMS/GCA correspondence.…”

“…Similar to usual 2d CFTs, one can find a Cardy-like formula for the entropy of states |h L , h M . This calculation was done in [14] and the final entropy for large h L and h M is…”

Flat-Space Chiral Gravity

“…Thus, the spectrum of the modes (17) consistently matches the spectrum of Virasoro descendants of the vacuum on the CFT side. In addition to the linearized spectrum it is of interest to look for non-perturbative states, basically the flat-space limit of BTZ black holes [23][24][25]. They are important contributions to the quantum gravity partition function and required for modular invariance [26].…”

Warped AdS3 black holes in higher derivative gravity theories

“…Flat Space [62,63], Hyperscaling [64] and Rindler [64,65] holography in 2+1 space-time dimensions, but also in higher dimensions [66]. So far, the matching between Bekenstein-Hawking and field theory entropies for WAdS 3 black holes has been performed on a case-by-case basis in specific theories admitting WAdS 3 spaces as a solution -these backgrounds do not solve the vacuum Einstein's equation, so they require including matter fields or higher curvature corrections (see e.g.…”