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Title: Tensor networks from kinematic space

Abstract

We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space — the geometry of CFT intervals. In holographic theories kinematic space becomes identified with the space of bulk geodesics studied in integral geometry. We argue that in these settings MERA is best viewed as a discretization of the space of bulk geodesics rather than of the bulk geometry itself. As a test of this kinematic proposal, we compare the MERA representation of the thermofield-double state with the space of geodesics in the two-sided BTZ geometry, obtaining a detailed agreement which includes the entwinement sector. In conclusion, we discuss how the kinematic proposal can be extended to excited states by generalizing MERA to a broader class of compression networks.

Authors:
 [1];  [1];  [1];  [2]
  1. Stanford Univ., Stanford, CA (United States)
  2. Stanford Univ., Menlo Park, CA (United States). SLAC National Accelerator Lab.
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1322104
Grant/Contract Number:
AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT correspondence; gauge-gravity correspondence

Citation Formats

Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, and Sully, James. Tensor networks from kinematic space. United States: N. p., 2016. Web. doi:10.1007/JHEP07(2016)100.
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, & Sully, James. Tensor networks from kinematic space. United States. doi:10.1007/JHEP07(2016)100.
Czech, Bartlomiej, Lamprou, Lampros, McCandlish, Samuel, and Sully, James. Wed . "Tensor networks from kinematic space". United States. doi:10.1007/JHEP07(2016)100. https://www.osti.gov/servlets/purl/1322104.
@article{osti_1322104,
title = {Tensor networks from kinematic space},
author = {Czech, Bartlomiej and Lamprou, Lampros and McCandlish, Samuel and Sully, James},
abstractNote = {We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space — the geometry of CFT intervals. In holographic theories kinematic space becomes identified with the space of bulk geodesics studied in integral geometry. We argue that in these settings MERA is best viewed as a discretization of the space of bulk geodesics rather than of the bulk geometry itself. As a test of this kinematic proposal, we compare the MERA representation of the thermofield-double state with the space of geodesics in the two-sided BTZ geometry, obtaining a detailed agreement which includes the entwinement sector. In conclusion, we discuss how the kinematic proposal can be extended to excited states by generalizing MERA to a broader class of compression networks.},
doi = {10.1007/JHEP07(2016)100},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2016,
place = {United States},
year = {Wed Jul 20 00:00:00 EDT 2016},
month = {Wed Jul 20 00:00:00 EDT 2016}
}

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Cited by: 22works
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