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arXiv · 1309.3610

Coarse-grained entropy and causal holographic information in AdS/CFT

William R. Kelly·Aron C. Wall
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Abstract

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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William R. Kelly, Aron C. Wall. 2014-04-01. Coarse-grained entropy and causal holographic information in AdS/CFT. https://doi.org/10.1007/jhep03(2014)118

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