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Title: Large-d phase transitions in holographic mutual information

Abstract

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, wheremore » analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.« less

Authors:
 [1];  [1];  [2];  [3]
  1. Univ. of California, Davis, CA (United States)
  2. Katholieke Univ. Leuven (Belgium)
  3. Stanford Univ., CA (United States)
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE; European Union's Horizon 2020; European Research Council (ERC); US Air Force Office of Scientific Research (AFOSR); Qubit Collaboration
OSTI Identifier:
1659667
Grant/Contract Number:  
SC0009999; 665501; ERC-2013-CoG 61673 HoloQosmos; SC0019380
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2020; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Gauge-gravity correspondence

Citation Formats

Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., and Sorce, Jonathan. Large-d phase transitions in holographic mutual information. United States: N. p., 2020. Web. doi:10.1007/jhep04(2020)173.
Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., & Sorce, Jonathan. Large-d phase transitions in holographic mutual information. United States. https://doi.org/10.1007/jhep04(2020)173
Colin-Ellerin, Sean, Hubeny, Veronika E., Niehoff, Benjamin E., and Sorce, Jonathan. Mon . "Large-d phase transitions in holographic mutual information". United States. https://doi.org/10.1007/jhep04(2020)173. https://www.osti.gov/servlets/purl/1659667.
@article{osti_1659667,
title = {Large-d phase transitions in holographic mutual information},
author = {Colin-Ellerin, Sean and Hubeny, Veronika E. and Niehoff, Benjamin E. and Sorce, Jonathan},
abstractNote = {In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in GN in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large-d, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large-d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large-d expansion.},
doi = {10.1007/jhep04(2020)173},
url = {https://www.osti.gov/biblio/1659667}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 4,
volume = 2020,
place = {United States},
year = {2020},
month = {4}
}

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