A note on entanglement entropy and quantum geometry

Abstract

It has been argued that the entropy which one is computing in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalising these computations to arbitrary spacetime dimensions D+1>2 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3+1 dimensions, this entropy is given by the Bekenstein-Hawking formula.

14 pages. v2: journal version. Comment added

References in corpus (43)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Entropy and Area
• The holographic principle
• Real Ashtekar Variables for Lorentzian Signature Space-times
• The Thermodynamics of Black Holes
• Quantum Spin Dynamics (QSD)
• Black Hole Entropy from Loop Quantum Gravity
• LQG vertex with finite Immirzi parameter
• Entanglement entropy of black holes
• Entropy of Lovelock Black Holes
• Isolated Horizons: Hamiltonian Evolution and the First Law
• Remarks on entanglement entropy for gauge fields
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Decomposition of entanglement entropy in lattice gauge theory
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• Black hole entropy and SU(2) Chern-Simons theory
• Counting surface states in the loop quantum gravity
• Black hole entropy from an SU(2)-invariant formulation of Type I isolated horizons
• Edge states in Gravity and Black Hole Physics
• Physics of Trans-Planckian Gravity
• Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC
• The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries
• Entanglement Entropy in Loop Quantum Gravity
• Black Hole Entropy from complex Ashtekar variables
• Einstein-Yang-Mills Isolated Horizons: Phase Space, Mechanics, Hair and Conjectures
• Quantum horizons and black hole entropy: Inclusion of distortion and rotation
• Do gauge fields really contribute negatively to black hole entropy?
• The strong and weak holographic principles
• Semiclassical quantisation of space-times with apparent horizons
• Edge States in Gauge Theories: Theory, Interpretations and Predictions
• Towards Loop Quantum Supergravity (LQSG)
• The imaginary part of the gravity action and black hole entropy
• Black hole entropy from loop quantum gravity in higher dimensions
• Generic isolated horizons in loop quantum gravity
• BF Theory Explanation of the Entropy for Non-rotating Isolated Horizons
• Edge States and Entanglement Entropy
• On the nature of black hole entropy
• Apparent horizons, black hole entropy and loop quantum gravity
• The imaginary part of the gravitational action at asymptotic boundaries and horizons
• Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of "light-slice" entropy
• Action and entanglement in gravity and field theory

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• Entanglement entropy of Bell-network states in LQG: Analytical and numerical results
• Entropy of black holes with arbitrary shapes in loop quantum gravity
• Area Law from Loop Quantum Gravity
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition
• Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity