Tensor networks from kinematic space
Abstract
We point out that the MERA network for the ground state of a 1+1dimensional 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 thermofielddouble state with the space of geodesics in the twosided 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:
 Stanford Univ., Stanford, CA (United States)
 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:
 AC0276SF00515
 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 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdSCFT correspondence; gaugegravity 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. 2016.
"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+1dimensional 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 thermofielddouble state with the space of geodesics in the twosided 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 = 2016,
month = 7
}
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