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Covariant Residual Entropy

Hubeny, Veronika E.

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Authors

Veronika E. Hubeny



Abstract

A recently explored interesting quantity in AdS/CFT, dubbed ‘residual entropy’, characterizes the amount of collective ignorance associated with either boundary observers restricted to finite time duration, or bulk observers who lack access to a certain spacetime region. However, the previously-proposed expression for this quantity involving variation of boundary entanglement entropy (subsequently renamed to ‘differential entropy’) works only in a severely restrictive context. We explain the key limitations, arguing that in general, differential entropy does not correspond to residual entropy. Given that the concept of residual entropy as collective ignorance transcends these limitations, we identify two correspondingly robust, covariantly-defined constructs: a ‘strip-wedge’ associated with boundary observers and a ‘rim wedge’ associated with bulk observers. These causal sets are well-defined in arbitrary time-dependent asymptotically AdS spacetimes in any number of dimensions. We discuss their relation, specifying a criterion for when these two constructs coincide, and prove an inclusion relation for a general case. We also speculate about the implications for residual entropy. Curiously, despite each construct admitting a well-defined finite quantity related to the areas of associated bulk surfaces, these quantities are not in one-to-one correspondence with the defining regions of unknown. This has nontrivial implications about holographic measures of quantum information.

Citation

Hubeny, V. E. (2014). Covariant Residual Entropy. Journal of High Energy Physics, 2014(9), Article 156. https://doi.org/10.1007/jhep09%282014%29156

Journal Article Type Article
Publication Date Sep 25, 2014
Deposit Date Oct 2, 2014
Publicly Available Date Mar 29, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 9
Article Number 156
DOI https://doi.org/10.1007/jhep09%282014%29156
Keywords Gauge-gravity correspondence, AdS-CFT Correspondence.
Related Public URLs http://arxiv.org/pdf/1406.4611.pdf

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Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.




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