Universal Corner Symmetry and the Orbit Method for Gravity

Abstract

A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners -- codimension-$2$ surfaces supporting Noether charges. It applies to both finite distance and asymptotic corners. In this paper, we study this algebra and its representations, via the coadjoint orbit method. We show that generic orbits of the universal algebra split into sub-orbits spanned by finite distance and asymptotic corner symmetries, such that the full universal symmetry algebra gives rise to a unified treatment of corners in a manifold. We then identify the geometric structure that captures these algebraic properties on corners, which is the Atiyah Lie algebroid associated to a principal $GL(2,\mathbb{R})⋉{\mathbb{R}}^2$-bundle. This structure is suggestive of the existence of a novel quantum gravitational theory which would unitarily glue such geometric structures, with spacetime geometries appearing as semi-classical configurations.

arXiv commentV2, published version (NPB)

References in corpus (46)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Asymptotic symmetries and subleading soft graviton theorem
• The BMS/GCA correspondence
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• Supertranslations and Superrotations at the Black Hole Horizon
• A holographic reduction of Minkowski space-time
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• A 2D Stress Tensor for 4D Gravity
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Carrollian Physics at the Black Hole Horizon
• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Flat holography and Carrollian fluids
• Carroll Structures, Null Geometry and Conformal Isometries
• Conformal Carroll groups
• Notes on the BMS group in three dimensions: I. Induced representations
• Spacetime structure near generic horizons and soft hair
• Local phase space and edge modes for diffeomorphism-invariant theories
• BMS Particles in Three Dimensions
• The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$
• Generalized BMS charge algebra
• Enhanced asymptotic symmetry algebra of AdS3
• Exploring the holographic principle in asymptotically flat spacetimes via the BMS group
• Rigorous steps towards holography in asymptotically flat spacetimes
• Coadjoint orbits of the Virasoro algebra and the global Liouville equation
• Embeddings and Integrable Charges for Extended Corner Symmetry
• Isolated Surfaces and Symmetries of Gravity
• Carrollian conservation laws and Ricci-flat gravity
• Gravity Degrees of Freedom on a Null Surface
• Holography in asymptotically flat space-times and the BMS group
• Lorentz-diffeomorphism edge modes in 3d gravity
• Two-dimensional fluids and their holographic duals
• Null Conservation Laws for Gravity
• Weyl Connections and their Role in Holography
• Weyl Charges in Asymptotically Locally AdS${}_3$ Spacetimes
• Planar Carrollean dynamics, and the Carroll quantum equation
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Lie algebroids, gauge theories, and compatible geometrical structures
• Connections on Lie algebroids and on derivation-based noncommutative geometry
• Holographic positive energy theorems in three-dimensional gravity
• Formulation of gauge theories on transitive Lie algebroids
• Lie Algebroids and the Geometry of Off-shell BRST
• Cartan Connections and Atiyah Lie Algebroids

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• Matrix Quantization of Gravitational Edge Modes
• Quantum Null Geometry and Gravity
• Quantum Reference Frames at the Boundary of Spacetime
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• Weyl-Ambient Geometries
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• Corner symmetry and quantum geometry
• Physical Representations of Corner Symmetries
• Quantum Corner Symmetry: Representations and Gluing
• Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
• Dynamical Edge Modes in Yang-Mills Theory
• On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• Corner Structure of Four-Dimensional General Relativity in the Coframe Formalism
• Semi-Classical Limit of Quantum Gravity on Corners
• De Sitter Horizon Edge Partition Functions
• Gravitons on Nariai Edges