Rindler/Contracted-CFT Correspondence

Abstract

Taking the flat-space limit (zero cosmological constant limit) of the Rindler-AdS spacetime yields the Rindler metric. According to the proposal of Flat/contracted-CFT correspondence, the flat-space limit on the bulk side of asymptotically AdS spacetimes corresponds to the contraction of the conformal field theory on the boundary. We use this proposal for the Rindler-AdS/CFT correspondence and propose a dual theory for the Rindler spacetime, which is a contracted conformal field theory (CCFT). We show that the two-dimensional CCFT symmetries exactly predict the same two-point functions that one may find by taking the flat-space limit of three-dimensional Rindler-AdS holographic results. Using the Flat/CCFT proposal, we also calculate the three-dimensional Rindler energy-momentum tensor. Since the near horizon geometry of non-extreme black holes has a Rindler part, we note that it is plausible to find a dual CCFT at the horizon of non-extreme black holes. By using our energy-momentum tensor, we find the correct mass of non-rotating BTZ and show that the Cardy-like formula for CCFT yields the Bekenstein-Hawking entropy of non-extreme BTZ. Our current work is the first step towards describing the entropy of non-extreme black holes in terms of CCFTs microstates which live on the horizon.

18 pages, V2: typos corrected, published version

References in corpus (31)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• The Kerr/CFT Correspondence
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• The BMS/GCA correspondence
• A New Cosmological Scenario in String Theory
• Holography of 3d Flat Cosmological Horizons
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• Asymptotic Structure of Symmetry Reduced General Relativity
• Conformal description of horizon's states
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Accelerated Detectors and Temperature in (Anti) de Sitter Spaces
• Flat-Space Chiral Gravity
• Higher spin theory in 3-dimensional flat space
• Mapping Hawking into Unruh Thermal Properties
• Asymptotically flat spacetimes in three-dimensional higher spin gravity
• Tensionless Strings and Galilean Conformal Algebra
• On Representations and Correlation Functions of Galilean Conformal Algebras
• Rindler Quantum Gravity
• 3D Flat Holography: Entropy and Logarithmic Corrections
• Cosmic evolution from phase transition of 3-dimensional flat space
• Equivalence of Hawking and Unruh Temperatures and Entropies Through Flat Space Embeddings
• Variational principle and 1-point functions in 3-dimensional flat space Einstein gravity
• A Grassmann Path From AdS_3 to Flat Space
• Flat-Space Energy-Momentum Tensor from BMS/GCA Correspondence
• Comment on "Accelerated Detectors and Temperature in (Anti) de Sitter Spaces"
• Non-relativistic CFT and Semi-classical Strings
• Flat/AdS boundary conditions in three dimensional conformal gravity
• Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence
• Extremal black holes, Holography & Coarse graining
• Fermions in non-relativistic AdS/CFT correspondence

Cited by in corpus (16)

• Entanglement Entropy in Flat Holography
• Near-Horizon Geometry and Warped Conformal Symmetry
• Black Hole Entropy from BMS Symmetry at the Horizon
• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Aspects of Flat/CCFT Correspondence
• Holography of 3D Asymptotically Flat Black Holes
• Flat-Space Holography and Stress Tensor of Kerr Black Hole
• First Law of Entanglement Entropy in Flat-Space Holography
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Universal sectors of two-dimensional Carrollian CFTs
• Canonical Quantization of the U(1) Gauge Field in the right Rindler-wedge in the Rindler Coordinates
• Canonical Quantization of the U(1) Gauge Field in the Rindler Coordinates
• The Static Heavy Quark-Antiquark Potential within String Theory in Arbitrary Stationary Backgrounds