http://arxiv.org/abs/1309.4523
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
Kristan Jensen, Andy O'Bannon
(Submitted on 18 Sep 2013)
We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT (BCFT) or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi-)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For BCFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein-Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi's conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the R\'enyi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.
http://arxiv.org/abs/1309.3610
Coarse-grained entropy and causal holographic information in AdS/CFT
William R. Kelly, Aron C. Wall
(Submitted on 14 Sep 2013)
We propose bulk duals for certain coarse-grained entropies of boundary regions. The `one-point entropy' is defined in the conformal field theory by maximizing the entropy in a domain of dependence while fixing the one-point functions. We conjecture that this is dual to the area of the edge of the region causally accessible to the domain of dependence (i.e. the `causal holographic information' of Hubeny and Rangamani). The `future one-point entropy' is defined by generalizing this conjecture to future domains of dependence and their corresponding bulk regions. We show that the future one-point entropy obeys a nontrivial second law. If our conjecture is true, this answers the question "What is the field theory dual of Hawking's area theorem?"
http://arxiv.org/abs/1309.4563
Statistics, holography 
, and black hole entropy in loop quantum gravity
Amit Ghosh, Karim Noui, Alejandro Perez
(Submitted on 18 Sep 2013)
In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or
punctures) labelled by spin ##j##. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area ##A## operator. On the other hand, the appropriately scaled area operator ##A/(8\pi\ell)## is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance ##\ell## from the horizon. Thus, the local energy is entirely accounted for by the geometric operator ##A##.
We assume that: In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of `matter' states is exponential with the area ##\exp{(\lambda A/\ell_p^2)}##---this is supported by the well established results of QFT in curved spacetimes, which do not determine ##\lambda## but asserts an exponential behaviour. The geometric excitations of the horizon (punctures) are indistinguishable. In the semiclassical limit the area of the black hole horizon is large in Planck units.
It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound,
viz. ##\lambda=\frac{1}{4}##. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy ##S={A}/({4\ell_p^2})##. The number of horizon punctures goes like ##N\propto \sqrt{A/\ell_p^2}##, i.e the number of punctures ##N## remains large in the semiclassical limit. Fluctuations of the horizon area are small while fluctuations of the area of an individual puncture are large. A precise notion of local conformal invariance of the thermal state is recovered in the ##A\to\infty## limit where the near horizon geometry becomes Rindler.
