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 (6)

• LQG vertex with finite Immirzi parameter
• Remarks on entanglement entropy for gauge fields
• Physics of Trans-Planckian Gravity
• Entanglement Entropy in Loop Quantum Gravity
• Generic isolated horizons in loop quantum gravity
• BF Theory Explanation of the Entropy for Non-rotating Isolated Horizons

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• 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