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Coarse-grained entropy and causal holographic information in AdS/CFT
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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?"
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Minimax surfaces and the holographic entropy cone
Stable minimax surfaces are shown to be HRT surfaces, the entanglement wedge is the smallest minimax homology region, and a cooperating time-sheet configuration would prove the equality of RT and HRT entropy cones.
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