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30
Quantum corrections to holographic entanglement entropy, JHEP 1311
, 2013
"... We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by RyuTakayanagi. Here we describe the one loop correction to this formula. The minimal surface divides t ..."
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We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by RyuTakayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.ar X iv
Entanglement Entropy in Scalar Field Theory,” J.Phys
 A46 (2013) 015402, arXiv:1209.4646 [hepth
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ADM reduction of Einstein action and black hole entropy,” arXiv:1304.0014 [hepth
"... We reduce the 4D EinsteinHilbert action to a constantradius hypersurface of foliation. The resulting theory is a scalar theory defined on a 3D hypersurface of the original black hole background, and has an exponential potential. Once the the hypersurface is located at the Schwarzschild radius, th ..."
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Cited by 6 (6 self)
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We reduce the 4D EinsteinHilbert action to a constantradius hypersurface of foliation. The resulting theory is a scalar theory defined on a 3D hypersurface of the original black hole background, and has an exponential potential. Once the the hypersurface is located at the Schwarzschild radius, the 3D theory is effectively reduced to a 2D Liouville type theory. We compute the entropy associated with the hypersurface intrinsic degrees of freedom, and show that its leading order reproduces the BekensteinHawking area law. The subleading terms come in logarithm/inverse powers of the area. ar X iv
Renyi Entropy and Geometry
 Phys. Rev. D
"... Entanglement entropy in even dimensional conformal field theories (CFTs) contains well– known universal terms arising from the conformal anomaly. Rényi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal ter ..."
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Cited by 2 (0 self)
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Entanglement entropy in even dimensional conformal field theories (CFTs) contains well– known universal terms arising from the conformal anomaly. Rényi entropies are natural generalizations of the entanglement entropy that are much less understood. Above two spacetime dimensions, the universal terms in the Rényi entropies are unknown for general entangling geometries. We conjecture a new structure in the dependence of the four–dimensional Rényi entropies on the intrinsic and extrinsic geometry of the entangling surface. We provide evidence for this conjecture by direct numerical computations in the free scalar and fermion field theories. The computation involves relating the four–dimensional free massless Rényi entropies across cylindrical entangling surfaces to corresponding three–dimensional massive Rényi entropies across circular entangling surfaces. Our numerical technique also allows us to directly probe other interesting aspects of threedimensional Rényi entropy, including the massless renormalized Rényi entropy and calculable contributions to the perimeter law.
Anomalies of the entanglement entropy in chiral theories
"... Abstract: We study entanglement entropy in theories with gravitational or mixed U(1) gaugegravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We disc ..."
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Abstract: We study entanglement entropy in theories with gravitational or mixed U(1) gaugegravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and selfdual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems. In two and four dimensions we use anomalous Ward identities to find general expressions for the transformation of the entanglement entropy under a diffeomorphism. (In the case of a mixed anomaly there is an alternative presentation of the theory in which the entanglement entropy is not invariant under a U(1) gauge transformation. The freefield manifestation of this phenomenon involves a novel kind of fermion zero mode on a gravitational background with a twist in the normal bundle to the entangling surface.) We also study ddimensional anomalous systems as the boundaries of d+1 dimensional gapped Hall phases. Here the full system is nonanomalous, but the boundary anomaly manifests itself in a change in the entanglement entropy when the boundary metric is sheared relative to the bulk.