Holographic Reconstruction of 3D Flat Space-Time

Abstract

We study asymptotically flat space-times in 3 dimensions for Einstein gravity near future null infinity and show that the boundary is described by Carrollian geometry. This is used to add sources to the BMS gauge corresponding to a non-trivial boundary metric in the sense of Carrollian geometry. We then solve the Einstein equations in a derivative expansion and derive a general set of equations that take the form of Ward identities. Next, it is shown that there is a well-posed variational problem at future null infinity without the need to add any boundary term. By varying the on-shell action with respect to the metric data of the boundary Carrollian geometry we are able to define a boundary energy-momentum tensor at future null infinity. We show that its diffeomorphism Ward identity is compatible with Einstein's equations. There is another Ward identity that states that the energy flux vanishes. It is this fact that is responsible for the enhancement of global symmetries to the full BMS${}_3$ algebra when we are dealing with constant boundary sources. Using a notion of generalized conformal boundary Killing vector we can construct all conserved BMS${}_3$ currents from the boundary energy-momentum tensor.

v3: clarifications added, matches published version

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• Galilean Conformal Algebras and AdS/CFT
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Cited by in corpus (61)

• Carrollian Perspective on Celestial Holography
• Flat Holography: Aspects of the dual field theory
• Flat holography and Carrollian fluids
• Scattering Amplitudes: Celestial and Carrollian
• Bridging Carrollian and Celestial Holography
• BMS Particles in Three Dimensions
• Field Theories with Conformal Carrollian Symmetry
• Carroll Expansion of General Relativity
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• AdS Witten Diagrams to Carrollian Correlators
• Magic Fermions: Carroll and Flat Bands
• Carrollian conservation laws and Ricci-flat gravity
• Carrollian Approach to $1+3$D Flat Holography
• Brown-York charges at null boundaries
• Limits of JT gravity
• Embedding Galilean and Carrollian geometries I. Gravitational waves
• Carroll black holes
• The tensionless path from closed to open strings
• Carroll covariant scalar fields in two dimensions
• Locality and anomalies in warped conformal field theory
• Inhomogeneous Tensionless Superstrings
• Boosting to BMS
• Holographic Lorentz and Carroll Frames
• Three-dimensional Spin-3 Theories Based on General Kinematical Algebras
• From CFTs to theories with Bondi-Metzner-Sachs symmetries: Complexity and out-of-time-ordered correlators
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• A Rindler Road to Carrollian Worldsheets
• Carroll fermions in two dimensions
• The Symmetries of the Carroll Superparticle
• One-Loop Quantum Effects in Carroll Scalars
• BMS4 Algebra, Its Stability and Deformations
• Non-Riemannian gravity actions from double field theory
• Homogeneous Nonrelativistic Geometries as Coset Spaces
• Non-Lorentzian Chaos and Cosmological Holography
• Galilean Gauge Theories from Null Reductions
• Carrollian Supersymmetry and SYK-like models
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Linking Past and Future Null Infinity in Three Dimensions
• BMS Field Theories and Weyl Anomaly
• Symmetry Resolution in non-Lorentzian Field Theories
• BMS Modular Diaries: Torus one-point function
• Quantization of Carrollian conformal scalar theories
• Stress tensors of 3d Carroll CFTs
• Extended Kinematical 3D Gravity Theories
• Non-Lorentzian Kač-Moody Algebras
• Stress Tensor Correlators of CCFT${}_2$ using Flat-Space Holography
• Galilean fermions: Classical and quantum aspects
• Kaluza-Klein reductions and AdS/Ricci-flat correspondence
• Asymptotic symmetries and geometry on the boundary in the first order formalism
• Carroll spinors
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Complexity growth of BTZ black hole in massive gravity with a null string
• Non-Lorentzian Supergravity and Kinematical Superalgebras
• Finite actions and asymptotic charges at null infinity for any spin
• Anisotropic conformal Carroll field theories and their gravity duals
• Chern-Simons Holography: Boundary Conditions, Contractions and Double Extensions for a Journey Beyond Anti-de Sitter
• Universal sectors of two-dimensional Carrollian CFTs
• Carrollian superconformal theories and super BMS
• Modular matrices of 2d Carrollian and warped CFTs
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity
• Symmetries and Asymptotically Flat Space