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

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?"

43 pages, 9 figures. v3: minor changes suggested by referee v2: added a few additional references

References in corpus (14)

• Towards a derivation of holographic entanglement entropy
• Quantum corrections to holographic entanglement entropy
• Global Structure of Five-dimensional BPS Fuzzballs
• Holographic entanglement plateaux
• Quasiclassical Coarse Graining and Thermodynamic Entropy
• The entropy of a hole in spacetime
• Quantum Renormalization Group and Holography
• Entropic Counterpart of Perturbative Einstein Equation
• Ten Proofs of the Generalized Second Law
• Extracting the bulk metric from boundary information in asymptotically AdS spacetimes
• Global properties of causal wedges in asymptotically AdS spacetimes
• Properties of Causal Holographic Information
• Numerical metric extraction in AdS/CFT
• Entanglement and Thermal Entropy of Gauge Fields

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