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Luty, “Renormalization of Entanglement Entropy and the Gravitational Effective Action,” arXiv:1302.1878 [hepth
"... The entanglement entropy associated with a spatial boundary in quantum field theory is UV divergent, with the leading term proportional to the area of the boundary. We show that, for a class of quantum states defined by a path integral, the CallanWilczek formula gives a renormalized geometrical def ..."
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The entanglement entropy associated with a spatial boundary in quantum field theory is UV divergent, with the leading term proportional to the area of the boundary. We show that, for a class of quantum states defined by a path integral, the CallanWilczek formula gives a renormalized geometrical definition of the entanglement entropy. In particular, UV divergences localized on the entangling surface do not contribute to the entanglement entropy. The leading contribution to the entanglement entropy is then given by the BekensteinHawking formula, and subleading UVsensitive contributions are given in terms of renormalized couplings of the gravitational effective action. These results hold even if the UVdivergent contribution to the entanglement entropy is negative, for example, in theories with nonminimal scalar couplings to gravity. We show that the subleading UVdivergent terms in the renormalized entanglement entropy depend nontrivially on the quantum state. We compute new subleading terms in the entanglement entropy and find agreement with the Wald entropy formula in all cases. We speculate that the entanglement entropy of an arbitrary spatial boundary may be a welldefined observable in quantum gravity. ar
Notes on Derivation of ’Generalized Gravitational Entropy
"... An alternative derivation of generalized gravitational entropy associated to codimension 2 ’entangling ’ hypersurfaces is given. The approach is similar to the JacobsonMyers ’Hamiltonian ’ method and it does not require computations on manifolds with conical singularities. It is demonstrated that ..."
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An alternative derivation of generalized gravitational entropy associated to codimension 2 ’entangling ’ hypersurfaces is given. The approach is similar to the JacobsonMyers ’Hamiltonian ’ method and it does not require computations on manifolds with conical singularities. It is demonstrated that the entangling surfaces should be extrema of the entropy functional. When our approach is applied to Lovelock theories of gravity the generalized entropy formula coincides with results derived by other methods. 1 ar
The entropy of a hole in spacetime
"... Copyright It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content licence (like ..."
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Copyright It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content licence (like
Preprint typeset in JHEP style HYPER VERSION arXiv:1304.nnnn [hepth] On Spacetime Entanglement
"... Abstract: We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the BekensteinHawking area law. Using holographic entanglement entropy calculations, we show that this idea is realized in the RandallSundru ..."
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Abstract: We examine the idea that in quantum gravity, the entanglement entropy of a general region should be finite and the leading contribution is given by the BekensteinHawking area law. Using holographic entanglement entropy calculations, we show that this idea is realized in the RandallSundrum II braneworld for sufficiently large regions in smoothly curved backgrounds. Extending the induced gravity action on the brane to include the curvaturesquared interactions, we show that the Wald entropy closely matches the expression describing the entanglement entropy. The difference is that for a general region, the latter includes terms involving the extrinsic curvature of the entangling surface, which do not appear in the Wald entropy. We also consider various limitations on the validity of these results. ar X iv