Gravitational edge modes: From Kac-Moody charges to Poincaré networks

Abstract

We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together through their interfaces, we focus on a single domain and its punctured 2D boundary. The punctures carry a ladder of Kac-Moody edge modes, whose 0-modes represent the electric and momentum charges while the higher modes describe the stringy vibration modes of the 1D-boundary around each puncture. In particular, this allows to identify missing observables in the discretization scheme used in loop quantum gravity and leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. In the limit where the tubes are contracted to 1D links and the string modes neglected, we do not just recover loop quantum gravity but obtain a more general structure: Poincaré charge networks, which carry a representation of the 3D diffeomorphism boundary charges on top of the $\mathrm{SU}(2)$ fluxes and gauge transformations.

43 pages + 11 pages (appendix & bibliography)

References in corpus (14)

• Superboost transitions, refraction memory and super-Lorentz charge algebra
• Black Hole Entropy and Soft Hair
• Coarse graining flow of spin foam intertwiners
• Intrinsic non-commutativity of closed string theory
• CFT/Gravity Correspondence on the Isolated Horizon
• Particles as Wilson lines of gravitational field
• Coarse graining as a representation change
• Horizon entropy with loop quantum gravity methods
• Chern-Simons theory, Stokes' Theorem, and the Duflo map
• Bubble Networks: Framed Discrete Geometry for Quantum Gravity
• Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy
• Superselection Sectors of Gravitational Subregions
• SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant
• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity

Cited by in corpus (36)

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• Extended corner symmetry, charge bracket and Einstein's equations
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Edge modes of gravity. Part III. Corner simplicity constraints
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations
• Boundary effects in General Relativity with tetrad variables
• Gravity from symmetry: Duality and impulsive waves
• Edge modes as reference frames and boundary actions from post-selection
• Extended actions, dynamics of edge modes, and entanglement entropy
• Edge modes as dynamical frames: charges from post-selection in generally covariant theories
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Dynamical Edge Modes and Entanglement in Maxwell Theory
• Origin of the quantum group symmetry in 3d quantum gravity
• Kinematical Gravitational Charge Algebra
• Quantum geometry from higher gauge theory
• Homological perspective on edge modes in linear Yang-Mills and Chern-Simons theory
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Gravitational $SL(2,\mathbb{R})$ Algebra on the Light Cone
• Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity
• The Cosmological Spinor
• Loop Quantum Gravity's Boundary Maps
• Corner symmetry and quantum geometry
• Soft edges: the many links between soft and edge modes
• Covariant Momentum Map Thermodynamics for Parametrized Field Theories
• The Quantum Gravity Disk: Discrete Current Algebra
• Twistor representation of Jackiw-Teitelboim gravity
• Quantum Corner Symmetry: Representations and Gluing
• Deformed Heisenberg charges in three-dimensional gravity
• Poincare group spin networks
• Macroscopic observables from the comparison of local reference systems
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• Dynamical Edge Modes in Yang-Mills Theory
• De Sitter Horizon Edge Partition Functions
• Gravitons on Nariai Edges