Local phase space and edge modes for diffeomorphism-invariant theories

Abstract

We discuss an approach to characterizing local degrees of freedom of a subregion in diffeomorphism-invariant theories using the extended phase space of Donnelly and Freidel, [JHEP 2016 (2016) 102]. Such a characterization is important for defining local observables and entanglement entropy in gravitational theories. Traditional phase space constructions for subregions are not invariant with respect to diffeomorphisms that act at the boundary. The extended phase space remedies this problem by introducing edge mode fields at the boundary whose transformations under diffeomorphisms render the extended symplectic structure fully gauge invariant. In this work, we present a general construction for the edge mode symplectic structure. We show that the new fields satisfy a surface symmetry algebra generated by the Noether charges associated with the edge mode fields. For surface-preserving symmetries, the algebra is universal for all diffeomorphism-invariant theories, comprised of diffeomorphisms of the boundary, $SL(2,\mathbb{R})$ transformations of the normal plane, and, in some cases, normal shearing transformations. We also show that if boundary conditions are chosen such that surface translations are symmetries, the algebra acquires a central extension.

29+12 pages, references added and minor typos fixed

References in corpus (10)

• Thermodynamical Property of Entanglement Entropy for Excited States
• Nonlinear Gravity from Entanglement in Conformal Field Theories
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Universality of Gravity from Entanglement
• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• Quantum Gravity on the Lattice
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Entanglement equilibrium for higher order gravity
• Newton constant, contact terms and entropy
• Ryu-Takayanagi Area as an Entanglement Edge Term

Cited by in corpus (91)

• Edge modes of gravity -- I: Corner potentials and charges
• Covariant phase space with boundaries
• Flat entanglement spectra in fixed-area states of quantum gravity
• Holographic Renyi Entropy from Quantum Error Correction
• Symmetries and charges of general relativity at null boundaries
• Extended corner symmetry, charge bracket and Einstein's equations
• Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Generalized entropy for general subregions in quantum gravity
• Embeddings and Integrable Charges for Extended Corner Symmetry
• Isolated Surfaces and Symmetries of Gravity
• Anomalies in gravitational charge algebras of null boundaries and black hole entropy
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Lorentz-diffeomorphism edge modes in 3d gravity
• Brown-York charges at null boundaries
• A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
• Null Conservation Laws for Gravity
• A general framework for gravitational charges and holographic renormalization
• Edge modes as reference frames and boundary actions from post-selection
• Gravitational edge modes: From Kac-Moody charges to Poincaré networks
• Universal Corner Symmetry and the Orbit Method for Gravity
• Extended actions, dynamics of edge modes, and entanglement entropy
• Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches
• Holographic Lorentz and Carroll Frames
• Edge modes as dynamical frames: charges from post-selection in generally covariant theories
• The Holographic Shape of Entanglement and Einstein's Equations
• Electromagnetic duality and central charge
• Soft Charges and Electric-Magnetic Duality
• Symmetries of the Black Hole Interior and Singularity Regularization
• The partial Bondi gauge: Gauge fixings and asymptotic charges
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Symmetries, charges and conservation laws at causal diamonds in general relativity
• Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more
• Ambiguity resolution for integrable gravitational charges
• Entanglement entropy of gravitational edge modes
• Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
• Matrix Quantization of Gravitational Edge Modes
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Quantum Reference Frames at the Boundary of Spacetime
• Entanglement entropy in Jackiw-Teitelboim Gravity
• Quantum Null Geometry and Gravity
• Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument
• Conformal boundary conditions, loop gravity and the continuum
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• Virasoro hair and entropy for axisymmetric Killing horizons
• Superselection Sectors of Gravitational Subregions
• Covariant canonical formulations of classical field theories
• Geometric relational framework for general-relativistic gauge field theories
• Symmetries and Charges in Weyl-Fefferman-Graham Gauge
• Edge modes without edge modes
• Area deficits and the Bel-Robinson tensor
• Virasoro Entanglement Berry Phases
• The Holographic Dual of the Entanglement Wedge Symplectic Form
• Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions
• Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence
• Unambiguous Phase Spaces for Subregions
• Entanglement Entropy, Relative Entropy and Duality
• Geometrical tools for embedding fields, submanifolds, and foliations
• An order-unity correction to Hawking radiation
• Gauge Is More Than Mathematical Redundancy
• The action of HRT-areas as operators in semiclassical gravity
• The dressing field method for diffeomorphisms: a relational framework
• Metriplectic geometry for gravitational subsystems
• Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy
• The quasilocal degrees of freedom of Yang-Mills theory
• Minimal Areas from Entangled Matrices
• A General Hierarchy of Charges at Null Infinity via the Todd Polynomials
• Subregions, Minimal Surfaces, and Entropy in Semiclassical Gravity
• Physical Representations of Corner Symmetries
• One-loop partition function of gravity with leaky boundary conditions
• On the first law of entanglement for Quasi-Topological gravity
• Soft thermodynamics of gravitational shock wave
• On the covariant formulation of gauge theories with boundaries
• Axialgravisolitons at infinite corners
• Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity
• Field-dependent diffeomorphisms and the transformation of surface charges between gauges
• Spacetime boundaries do not break diffeomorphism and gauge symmetries
• Dynamical Edge Modes in Yang-Mills Theory
• Entanglement Entropy in Closed String Theory
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs
• Singular Supertranslations and Chern-Simons Theory on the Black Hole Horizon
• On the Charge Algebra of Causal Diamonds in Three Dimensional Gravity
• De Sitter Horizon Edge Partition Functions
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Covariant phase space with null boundaries
• Notes on a few quasilocal properties of Yang-Mills theory
• Gravitons on Nariai Edges
• The classical dynamics of gauge theories in the deep infrared
• A canonical bracket for open gravitational system
• Mechanics as a general-relativistic gauge field theory, and Relational Quantization
• The integrability of Virasoro charges for axisymmetric Killing horizons