Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes

Abstract

We discuss an enhancement of the Brown-Henneaux boundary conditions in three-dimensional AdS General Relativity to encompass Weyl transformations of the boundary metric. The resulting asymptotic symmetry algebra, after a field-dependent redefinition of the generators, is a direct sum of two copies of the Witt algebra and the Weyl abelian sector. The charges associated to Weyl transformations are non-vanishing, integrable but not conserved due to a flux driven by the Weyl anomaly coefficient. The charge algebra admits an additional non-trivial central extension in the Weyl sector, related to the well-known Weyl anomaly. We then construct the holographic Weyl current and show that it satisfies an anomalous Ward-Takahashi identity of the boundary theory.

arXiv comment29 pages, Latex, V2, Minor Revisions

References in corpus (81)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The World as a Hologram
• The Black Hole in Three Dimensional Space Time
• 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
• Geometry of the 2+1 Black Hole
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• Black Hole Entropy from Near-Horizon Microstates
• Holographic Renormalization
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Aspects of the BMS/CFT correspondence
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Twenty Years of the Weyl Anomaly
• The (2+1)-Dimensional Black Hole
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• Three-Dimensional Gravity Revisited
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• 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
• Quantum effective action from the AdS/CFT correspondence
• Asymptotically Anti-de Sitter spacetimes and their stress energy tensor
• Diffeomorphisms and Holographic Anomalies
• Weyl Cohomology and the Effective Action for Conformal Anomalies
• Global Charges in Chern-Simons theory and the 2+1 black hole
• Flat holography and Carrollian fluids
• Entanglement Entropy, Trace Anomalies and Holography
• New Boundary Conditions for AdS3
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• Edge modes of gravity -- I: Corner potentials and charges
• Covariant phase space with boundaries
• The $\Lambda$-BMS${}_4$ Charge Algebra
• BMS Particles in Three Dimensions
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Asymptotic Symmetries and Celestial CFT
• Most general AdS_3 boundary conditions
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Enhanced asymptotic symmetry algebra of AdS3
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Exploring the holographic principle in asymptotically flat spacetimes via the BMS group
• Most general flat space boundary conditions in three-dimensional Einstein gravity
• Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity
• Rigorous steps towards holography in asymptotically flat spacetimes
• Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Uplifting AdS3/CFT2 to Flat Space Holography
• A short review on Noether's theorems, gauge symmetries and boundary terms
• Two-dimensional fluids and their holographic duals
• Algebraic Classification of Weyl Anomalies in Arbitrary Dimensions
• An sl(2, R) current algebra from AdS_3 gravity
• Dynamics of Asymptotic Diffeomorphisms in (2+1)-Dimensional Gravity
• Lectures on Anomalies
• (A)dS${}_4$ in Bondi gauge
• Diffeomorphisms, Anomalies and the Fefferman-Graham Ambiguity
• General solutions of the Wess-Zumino consistency condition for the Weyl anomalies
• BMS current algebra in the context of the Newman-Penrose formalism
• A Non-Relativistic Weyl Anomaly
• On the structure and applications of the Bondi-Metzner-Sachs group
• Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity
• Weyl Connections and their Role in Holography
• Counterterms, Kounterterms, and the variational problem in AdS gravity
• Holographic Renormalisation and Anomalies
• Counterterms and dual holographic anomalies in CS gravity
• Gauges in Three-Dimensional Gravity and Holographic Fluids
• Holographic currents in first order Gravity and finite Fefferman-Graham expansions
• Uniqueness of the asymptotic AdS3 geometry
• Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups
• Asymptotic dynamics of AdS${}_3$ gravity with two asymptotic regions
• Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background
• Covariant Charges in Chern-Simons AdS_3 Gravity
• On asymptotic charges in 3D gravity
• Quantum BMS transformations in conformally flat space-times and holography
• Holographic Trace Anomaly and Cocycle of Weyl Group
• Note on the symplectic structure of asymptotically flat gravity and BMS symmetries

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• The partial Bondi gauge: Further enlarging the asymptotic structure of gravity
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• Conservation and Integrability in Lower-Dimensional Gravity
• Universal Corner Symmetry and the Orbit Method for Gravity
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• Symmetries at Causal Boundaries in 2D and 3D Gravity
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• 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability
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• Hydro & Thermo Dynamics at Causal Boundaries, Examples in 3d Gravity
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• One-loop partition function of gravity with leaky boundary conditions
• Twisting asymptotic symmetries and algebraically special vacuum solutions
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• 1/c deformations of AdS${}_3$ boundary conditions and the Dym hierarchy
• Boundary Conditions for Warped AdS${}_3$ in Quadratic Ensemble