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.

V2, published version (NPB)

References in corpus (11)

• Asymptotic symmetries and subleading soft graviton theorem
• The BMS/GCA correspondence
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Conformal Carroll groups
• Notes on the BMS group in three dimensions: I. Induced representations
• Embeddings and Integrable Charges for Extended Corner Symmetry
• Isolated Surfaces and Symmetries of Gravity
• Planar Carrollean dynamics, and the Carroll quantum equation
• Near-Horizon BMS Symmetry, Dimensional Reduction, and Black Hole Entropy
• Holographic positive energy theorems in three-dimensional gravity
• Formulation of gauge theories on transitive Lie algebroids

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• 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
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• 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