Charge Algebra in Al(A)dS${}_n$ Spacetimes

Abstract

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in $n$ dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent $2$-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the $2$-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the $\Lambda$-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in $n$ dimensions.

arXiv comment48 pages, 1 figure, published version

References in corpus (119)

• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• A Stress Tensor for Anti-de Sitter Gravity
• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• The dS/CFT Correspondence
• Black Hole Entropy from Near-Horizon Microstates
• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of Hawking radiation
• Holographic Renormalization
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Aspects of the BMS/CFT correspondence
• Single field consistency relation for the 3-point function
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Asymptotically Anti-de Sitter Space-times: Conserved Quantities
• BMS charge algebra
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• Asymptotic symmetries and subleading soft graviton theorem
• Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions
• Setting the boundary free in AdS/CFT
• Surface charge algebra in gauge theories and thermodynamic integrability
• The flat limit of three dimensional asymptotically anti-de Sitter spacetimes
• Diffeomorphisms and Holographic Anomalies
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• Conserved charges of the extended Bondi-Metzner-Sachs algebra
• On the consistency relation of the 3-point function in single field inflation
• New symmetries for the Gravitational S-matrix
• Islands outside the horizon
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Entanglement Entropy, Trace Anomalies and Holography
• New Boundary Conditions for AdS3
• Quadratic Gravity
• Conformally Soft Photons and Gravitons
• Edge modes of gravity -- I: Corner potentials and charges
• Extended Symmetries at the Black Hole Horizon
• Covariant phase space with boundaries
• An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology
• Boundary charges in gauge theories: using Stokes theorem in the bulk
• Celestial amplitudes and conformal soft theorems
• The $\Lambda$-BMS${}_4$ Charge Algebra
• Statistical Entropy of Three-dimensional Kerr-De Sitter Space
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Asymptotic Symmetries and Celestial CFT
• Asymptotics with a positive cosmological constant: I. Basic framework
• Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem
• Most general AdS_3 boundary conditions
• Conserved Charges for Even Dimensional Asymptotically AdS Gravity Theories
• Generalized BMS charge algebra
• The Holographic Nature of Null Infinity
• Enhanced asymptotic symmetry algebra of AdS3
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• BMS Supertranslations and Memory in Four and Higher Dimensions
• The Poincaré and BMS flux-balance laws with application to binary systems
• Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity
• Lectures on Integrability of Lie Brackets
• Null infinity, the BMS group and infrared issues
• Extended BMS Algebra of Celestial CFT
• Boundary conditions for General Relativity on AdS${}_3$ and the KdV hierarchy
• Asymptotic Symmetries and Charges in De Sitter Space
• Einstein-Yang-Mills theory : I. Asymptotic symmetries
• Edge modes of gravity. Part III. Corner simplicity constraints
• BMS Symmetry of Celestial OPE
• Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Extended Super BMS Algebra of Celestial CFT
• Slavnov-Taylor Identities for Primordial Perturbations
• Open quantum systems and Schwinger-Keldysh holograms
• Uplifting AdS3/CFT2 to Flat Space Holography
• Double Copy for Celestial Amplitudes
• Two-dimensional fluids and their holographic duals
• Conformal Null Infinity Does Not Exist for Radiating Solutions in Odd Spacetime Dimensions
• Gravitational Memory in Higher Dimensions
• The Soft $\mathcal{S}$-Matrix in Gravity
• (A)dS${}_4$ in Bondi gauge
• Centrally extended BMS4 Lie algebroid
• BMS in Cosmology
• The Cosmological Memory Effect
• T-Witts from the horizon
• Soft-Pion Theorems for Large Scale Structure
• BMS current algebra in the context of the Newman-Penrose formalism
• Loops on the Celestial Sphere
• Inflationary soft theorems revisited: A generalized consistency relation
• Gravitational wave memory in $\Lambda$CDM cosmology
• Gravitational wave memory in de Sitter spacetime
• Weyl Connections and their Role in Holography
• Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes
• A note on gauge systems from the point of view of Lie algebroids
• Subleading BMS charges and fake news near null infinity
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Extensions of the asymptotic symmetry algebra of general relativity
• The Effective Action of Superrotation Modes
• Gravitational Wave Memory In dS${}_{4+2n}$ and 4D Cosmology
• Future Boundary Conditions in De Sitter Space
• Memory in de Sitter space and BMS-like supertranslations
• Transverse-Traceless Gravitational Waves In A Spatially Flat FLRW Universe: Causal Structure from Dimension Reduction
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Free boundary conditions and the AdS${}_3$/CFT${}_2$ correspondence
• More On Cosmological Gravitational Waves And Their Memories
• Asymptotics with a positive cosmological constant: IV. The `no-incoming radiation' condition
• Supertranslations in Higher Dimensions Revisited
• Hamiltonian surface charges using external sources
• Asymptotic symmetries and subleading soft graviton theorem in higher dimensions
• Weinberg Soft Theorems from Weinberg Adiabatic Modes
• Quantum BMS transformations in conformally flat space-times and holography
• Conserved charges in asymptotically de Sitter spacetimes
• Boundary Conditions and Vacuum Fluctuations in ${\mathrm{AdS}}_4$
• Memory Effect in Anti-de Sitter Spacetime
• On the Various Extensions of the BMS Group
• Holography and unitarity
• Introduction to Classical Gauge Field Theory and to Batalin-Vilkovisky Quantization
• Gravitational Corner Conditions in Holography
• Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit
• Covariant Symplectic Structure and Conserved Charges of New Massive Gravity
• BMS Symmetry via AdS/CFT

Cited by in corpus (20)

• Carrollian Perspective on Celestial Holography
• Bridging Carrollian and Celestial Holography
• The Weyl BMS group and Einstein's equations
• Extended corner symmetry, charge bracket and Einstein's equations
• Null boundary phase space: slicings, news and memory
• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• A general framework for gravitational charges and holographic renormalization
• Holographic Lorentz and Carroll Frames
• Celestial Holography: Lectures on Asymptotic Symmetries
• Tractor geometry of asymptotically flat spacetimes
• Holographic boundary actions in AdS${}_3$/CFT${}_2$ revisited
• Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics
• $1/L^2$ corrected soft photon theorem from a CFT${}_3$ Ward identity
• Charges, conserved quantities and fluxes in de Sitter spacetime
• AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula
• Irrelevant Operators and their Holographic Anomalies
• $p$-Form Surface Charges on AdS: Renormalization and Conservation
• The integrability of Virasoro charges for axisymmetric Killing horizons
• The Kerr-de Sitter spacetime in Bondi coordinates