Link-area commutators in AdS_3$ area-networks
Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region $R$ and its complement $\bar R$, standard RTNs are most analogous to fixed-area states of the bulk quantum gravity...
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creator | Held, Jesse Kaplan, Molly Marolf, Donald Wu, Jie-qiang |
description | Random tensor networks (RTNs) have proved to be fruitful tools for modelling
the AdS/CFT correspondence. Due to their flat entanglement spectra, when
discussing a given boundary region $R$ and its complement $\bar R$, standard
RTNs are most analogous to fixed-area states of the bulk quantum gravity
theory, in which quantum fluctuations have been suppressed for the area of the
corresponding HRT surface. However, such RTNs have flat entanglement spectra
for all choices of $R, \bar R,$ while quantum fluctuations of multiple
HRT-areas can be suppressed only when the corresponding HRT-area operators
mutually commute. We probe the severity of such obstructions in pure AdS$_3$
Einstein-Hilbert gravity by constructing networks whose links are codimension-2
extremal-surfaces and by explicitly computing semiclassical commutators of the
associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are
geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link
network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT
surface for which all link-areas commute. However, the algebra generated by the
link-areas of more general networks tends to be non-Abelian. One such
non-Abelian example is associated with entanglement-wedge cross sections and
may be of more general interest. |
doi_str_mv | 10.48550/arxiv.2401.02487 |
format | Article |
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the AdS/CFT correspondence. Due to their flat entanglement spectra, when
discussing a given boundary region $R$ and its complement $\bar R$, standard
RTNs are most analogous to fixed-area states of the bulk quantum gravity
theory, in which quantum fluctuations have been suppressed for the area of the
corresponding HRT surface. However, such RTNs have flat entanglement spectra
for all choices of $R, \bar R,$ while quantum fluctuations of multiple
HRT-areas can be suppressed only when the corresponding HRT-area operators
mutually commute. We probe the severity of such obstructions in pure AdS$_3$
Einstein-Hilbert gravity by constructing networks whose links are codimension-2
extremal-surfaces and by explicitly computing semiclassical commutators of the
associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are
geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link
network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT
surface for which all link-areas commute. However, the algebra generated by the
link-areas of more general networks tends to be non-Abelian. One such
non-Abelian example is associated with entanglement-wedge cross sections and
may be of more general interest.</description><identifier>DOI: 10.48550/arxiv.2401.02487</identifier><language>eng</language><subject>Physics - General Relativity and Quantum Cosmology ; Physics - High Energy Physics - Theory</subject><creationdate>2024-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2401.02487$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2401.02487$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Held, Jesse</creatorcontrib><creatorcontrib>Kaplan, Molly</creatorcontrib><creatorcontrib>Marolf, Donald</creatorcontrib><creatorcontrib>Wu, Jie-qiang</creatorcontrib><title>Link-area commutators in AdS_3$ area-networks</title><description>Random tensor networks (RTNs) have proved to be fruitful tools for modelling
the AdS/CFT correspondence. Due to their flat entanglement spectra, when
discussing a given boundary region $R$ and its complement $\bar R$, standard
RTNs are most analogous to fixed-area states of the bulk quantum gravity
theory, in which quantum fluctuations have been suppressed for the area of the
corresponding HRT surface. However, such RTNs have flat entanglement spectra
for all choices of $R, \bar R,$ while quantum fluctuations of multiple
HRT-areas can be suppressed only when the corresponding HRT-area operators
mutually commute. We probe the severity of such obstructions in pure AdS$_3$
Einstein-Hilbert gravity by constructing networks whose links are codimension-2
extremal-surfaces and by explicitly computing semiclassical commutators of the
associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are
geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link
network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT
surface for which all link-areas commute. However, the algebra generated by the
link-areas of more general networks tends to be non-Abelian. One such
non-Abelian example is associated with entanglement-wedge cross sections and
may be of more general interest.</description><subject>Physics - General Relativity and Quantum Cosmology</subject><subject>Physics - High Energy Physics - Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj1vwjAUhWEvHVDoD2AiA6vTa18ntkeEWkCKxAB7dBNsKQpJKifQ8u_5nM7wSkcPYzMBiTJpCl8U_utLIhWIBKQyesJ4XncNp-Aorvq2PY809mGI6y5eHvcFLuJH4p0b__rQDFP24ek0uM_3Ruzw831YbXi-W29Xy5xTpjXHkkhYjdYROJQE4DKJxoMi1FDJUih79EroUhlnhfDqrrM-q1CCMNZhxOav26e3-A11S-FaPNzF0403uLk7QQ</recordid><startdate>20240104</startdate><enddate>20240104</enddate><creator>Held, Jesse</creator><creator>Kaplan, Molly</creator><creator>Marolf, Donald</creator><creator>Wu, Jie-qiang</creator><scope>GOX</scope></search><sort><creationdate>20240104</creationdate><title>Link-area commutators in AdS_3$ area-networks</title><author>Held, Jesse ; Kaplan, Molly ; Marolf, Donald ; Wu, Jie-qiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-3baa19739ea0e32a00e6238f04a370c2b149df417b48e911f44859f6c320189e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Physics - General Relativity and Quantum Cosmology</topic><topic>Physics - High Energy Physics - Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Held, Jesse</creatorcontrib><creatorcontrib>Kaplan, Molly</creatorcontrib><creatorcontrib>Marolf, Donald</creatorcontrib><creatorcontrib>Wu, Jie-qiang</creatorcontrib><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Held, Jesse</au><au>Kaplan, Molly</au><au>Marolf, Donald</au><au>Wu, Jie-qiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Link-area commutators in AdS_3$ area-networks</atitle><date>2024-01-04</date><risdate>2024</risdate><abstract>Random tensor networks (RTNs) have proved to be fruitful tools for modelling
the AdS/CFT correspondence. Due to their flat entanglement spectra, when
discussing a given boundary region $R$ and its complement $\bar R$, standard
RTNs are most analogous to fixed-area states of the bulk quantum gravity
theory, in which quantum fluctuations have been suppressed for the area of the
corresponding HRT surface. However, such RTNs have flat entanglement spectra
for all choices of $R, \bar R,$ while quantum fluctuations of multiple
HRT-areas can be suppressed only when the corresponding HRT-area operators
mutually commute. We probe the severity of such obstructions in pure AdS$_3$
Einstein-Hilbert gravity by constructing networks whose links are codimension-2
extremal-surfaces and by explicitly computing semiclassical commutators of the
associated link-areas. Since $d=3,$ codimension-2 extremal-surfaces are
geodesics, and codimension-2 `areas' are lengths. We find a simple 4-link
network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT
surface for which all link-areas commute. However, the algebra generated by the
link-areas of more general networks tends to be non-Abelian. One such
non-Abelian example is associated with entanglement-wedge cross sections and
may be of more general interest.</abstract><doi>10.48550/arxiv.2401.02487</doi><oa>free_for_read</oa></addata></record> |
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subjects | Physics - General Relativity and Quantum Cosmology Physics - High Energy Physics - Theory |
title | Link-area commutators in AdS_3$ area-networks |
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