The gravity dual of Rényi entropy
Abstract
A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gaugegravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a oneparameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.
 Authors:
 Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
 Publication Date:
 Research Org.:
 Princeton Univ., NJ (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC); National Science Foundation (NSF)
 OSTI Identifier:
 1358548
 Grant/Contract Number:
 SC0009988
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Nature Communications
 Additional Journal Information:
 Journal Volume: 7; Journal ID: ISSN 20411723
 Publisher:
 Nature Publishing Group
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Dong, Xi. The gravity dual of Rényi entropy. United States: N. p., 2016.
Web. doi:10.1038/ncomms12472.
Dong, Xi. The gravity dual of Rényi entropy. United States. doi:10.1038/ncomms12472.
Dong, Xi. 2016.
"The gravity dual of Rényi entropy". United States.
doi:10.1038/ncomms12472. https://www.osti.gov/servlets/purl/1358548.
@article{osti_1358548,
title = {The gravity dual of Rényi entropy},
author = {Dong, Xi},
abstractNote = {A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gaugegravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a oneparameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.},
doi = {10.1038/ncomms12472},
journal = {Nature Communications},
number = ,
volume = 7,
place = {United States},
year = 2016,
month = 8
}
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