On 3d Bulk Geometry of Virasoro Coadjoint Orbits: Orbit invariant charges and Virasoro hair on locally AdS3 geometries

Abstract

Expanding upon [arXiv:1404.4472, 1511.06079], we provide further detailed analysis of Bañados geometries, the most general solutions to the AdS3 Einstein gravity with Brown-Henneaux boundary conditions. We analyze in some detail the causal, horizon and boundary structure, and geodesic motion on these geometries, as well as the two class of symplectic charges one can associate with these geometries: charges associated with the exact symmetries and the Virasoro charges. We elaborate further the one-to-one relation between the coadjoint orbits of two copies of Virasoro group and Bañados geometries. We discuss that the information about the Bañados goemetries fall into two categories: "orbit invariant" information and "Virasoro hairs". The former are geometric quantities while the latter are specified by the non-local surface integrals. We elaborate on multi-BTZ geometries which have some number of disconnected pieces at the horizon bifurcation curve. We study multi-BTZ black hole thermodynamics and discuss that the thermodynamic quantities are orbit invariants. We also comment on the implications of our analysis for a 2d CFT dual which could possibly be dual to AdS3 Einstein gravity.

36 pages, 4 figures, minor modification, references added

References in corpus (7)

• Three-Dimensional Gravity Revisited
• Notes on the BMS group in three dimensions: I. Induced representations
• Notes on the BMS group in three dimensions: II. Coadjoint representation
• Quantization of conical spaces in 3D gravity
• Holographic positive energy theorems in three-dimensional gravity
• Classification of Boundary Gravitons in AdS${}_3$ Gravity
• Orientifolded Locally AdS3 Geometries

Cited by in corpus (34)

• Superrotation Charge and Supertranslation Hair on Black Holes
• BMS Particles in Three Dimensions
• Soft hairy horizons in three spacetime dimensions
• Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes
• Complexity measures from geometric actions on Virasoro and Kac-Moody orbits
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Horizon fluff, semi-classical black hole microstates - Log-corrections to BTZ entropy and black hole/particle correspondence
• Geometric actions and flat space holography
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Comments on Thermalization in 2D CFT
• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Generic AdS3 Black Holes
• Multi-centered AdS${}_3$ solutions from Virasoro conformal blocks
• Excitation Entanglement Entropy in 2d Conformal Field Theories
• Calibrated Entanglement Entropy
• Exploring the Membrane Theory of Entanglement Dynamics
• Interpolating Between Asymptotic and Near Horizon Symmetries
• Soft hairs on isolated horizon implanted by electromagnetic fields
• Berry phases, wormholes and factorization in AdS/CFT
• Quantum thermodynamics of holographic quenches and bounds on the growth of entanglement from the QNEC
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Strolling along gauge theory vacua
• Hartle-Hawking state and its factorization in 3d gravity
• Holographic integral geometry with time dependence
• On the entanglement contour of excited states in the holographic CFT
• On the universality of late-time correlators in semi-classical 2d CFTs
• Vacuum block thermalization in semi-classical 2d CFT
• Banados and SUSY: On Supersymmetry and Minimal Surfaces of Locally AdS3 Geometries
• Extreme Kerr black hole microstates with horizon fluff
• Sliding Surface Charges on AdS${}_3$
• Warped Flatland
• Generalized Clausius inequalities and entanglement production in holographic two-dimensional CFTs
• Entanglement Entropy and Conformal Collider Physics in 2D CFTs
• Near-Horizon Extremal Geometries: Coadjoint Orbits and Quantization