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A bulk manifestation of Krylov complexity
A bstract There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely...
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| Published in: | The journal of high energy physics 2023-08, Vol.2023 (8), p.213-53, Article 213 |
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| Main Authors: | , , , |
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| cited_by | cdi_FETCH-LOGICAL-c445t-481163431bd11f8d773bff5af1fb64a04095e35e725344881cca12493f59bb4c3 |
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| cites | cdi_FETCH-LOGICAL-c445t-481163431bd11f8d773bff5af1fb64a04095e35e725344881cca12493f59bb4c3 |
| container_end_page | 53 |
| container_issue | 8 |
| container_start_page | 213 |
| container_title | The journal of high energy physics |
| container_volume | 2023 |
| creator | Rabinovici, E. Sánchez-Garrido, A. Shir, R. Sonner, J. |
| description | A
bstract
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS
2
. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS
2
has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space. |
| doi_str_mv | 10.1007/JHEP08(2023)213 |
| format | article |
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bstract
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS
2
. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS
2
has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.</description><identifier>ISSN: 1029-8479</identifier><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP08(2023)213</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>2D Gravity ; AdS-CFT Correspondence ; Black Holes ; Boundary maps ; Classical and Quantum Gravitation ; Complexity ; Eigenvectors ; Elementary Particles ; Field Theories in Lower Dimensions ; Gravitation theory ; High energy physics ; Hilbert space ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum Field Theories ; Quantum Field Theory ; Quantum Physics ; Quantum theory ; Regular Article - Theoretical Physics ; Relativity Theory ; String Theory</subject><ispartof>The journal of high energy physics, 2023-08, Vol.2023 (8), p.213-53, Article 213</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c445t-481163431bd11f8d773bff5af1fb64a04095e35e725344881cca12493f59bb4c3</citedby><cites>FETCH-LOGICAL-c445t-481163431bd11f8d773bff5af1fb64a04095e35e725344881cca12493f59bb4c3</cites><orcidid>0000-0003-2248-6913</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2859385926/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2859385926?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590,74998</link.rule.ids></links><search><creatorcontrib>Rabinovici, E.</creatorcontrib><creatorcontrib>Sánchez-Garrido, A.</creatorcontrib><creatorcontrib>Shir, R.</creatorcontrib><creatorcontrib>Sonner, J.</creatorcontrib><title>A bulk manifestation of Krylov complexity</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS
2
. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS
2
has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.</description><subject>2D Gravity</subject><subject>AdS-CFT Correspondence</subject><subject>Black Holes</subject><subject>Boundary maps</subject><subject>Classical and Quantum Gravitation</subject><subject>Complexity</subject><subject>Eigenvectors</subject><subject>Elementary Particles</subject><subject>Field Theories in Lower Dimensions</subject><subject>Gravitation theory</subject><subject>High energy physics</subject><subject>Hilbert space</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Quantum theory</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>String Theory</subject><issn>1029-8479</issn><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp9kb1PwzAUxC0EEqUws0ZigSHUzx91PFZVoYVKMMBs2Y5dpaR1cVJE_3tcgoAFBttP1t1P93QInQO-BozF4G46ecTFJcGEXhGgB6gHmMi8YEIe_pqP0UnTLDEGDhL30NUoM9v6JVvpdeVd0-q2Cuss-Ow-7urwltmw2tTuvWp3p-jI67pxZ19vHz3fTJ7G03z-cDsbj-a5ZYy3OSsAhpRRMCWAL0ohqPGeaw_eDJnGDEvuKHeCcMpYUYC1GgiT1HNpDLO0j2Ydtwx6qTaxWum4U0FX6vMjxIXSsa1s7ZRhRNhSS09JybwThlBBWJluV8pES6yLjrWJ4XWb1lPLsI3rFF-RoqAgBMfsfxWXNB0yTKpBp7IxNE10_jsbYLVvQHUNqH0DKjWQHLhzNEm5Xrj4w_3L8gH_kITa</recordid><startdate>20230831</startdate><enddate>20230831</enddate><creator>Rabinovici, E.</creator><creator>Sánchez-Garrido, A.</creator><creator>Shir, R.</creator><creator>Sonner, J.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-2248-6913</orcidid></search><sort><creationdate>20230831</creationdate><title>A bulk manifestation of Krylov complexity</title><author>Rabinovici, E. ; Sánchez-Garrido, A. ; Shir, R. ; Sonner, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c445t-481163431bd11f8d773bff5af1fb64a04095e35e725344881cca12493f59bb4c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>2D Gravity</topic><topic>AdS-CFT Correspondence</topic><topic>Black Holes</topic><topic>Boundary maps</topic><topic>Classical and Quantum Gravitation</topic><topic>Complexity</topic><topic>Eigenvectors</topic><topic>Elementary Particles</topic><topic>Field Theories in Lower Dimensions</topic><topic>Gravitation theory</topic><topic>High energy physics</topic><topic>Hilbert space</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theories</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Quantum theory</topic><topic>Regular Article - Theoretical Physics</topic><topic>Relativity Theory</topic><topic>String Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rabinovici, E.</creatorcontrib><creatorcontrib>Sánchez-Garrido, A.</creatorcontrib><creatorcontrib>Shir, R.</creatorcontrib><creatorcontrib>Sonner, J.</creatorcontrib><collection>SpringerOpen</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>The journal of high energy physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rabinovici, E.</au><au>Sánchez-Garrido, A.</au><au>Shir, R.</au><au>Sonner, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A bulk manifestation of Krylov complexity</atitle><jtitle>The journal of high energy physics</jtitle><stitle>J. 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bstract
There are various definitions of the concept of complexity in Quantum Field Theory as well as for finite quantum systems. For several of them there are conjectured holographic bulk duals. In this work we establish an entry in the AdS/CFT dictionary for one such class of complexity, namely Krylov or K-complexity. For this purpose we work in the double-scaled SYK model which is dual in a certain limit to JT gravity, a theory of gravity in AdS
2
. In particular, states on the boundary have a clear geometrical definition in the bulk. We use this result to show that Krylov complexity of the infinite-temperature thermofield double state on the boundary of AdS
2
has a precise bulk description in JT gravity, namely the length of the two-sided wormhole. We do this by showing that the Krylov basis elements, which are eigenstates of the Krylov complexity operator, are mapped to length eigenstates in the bulk theory by subjecting K-complexity to the bulk-boundary map identifying the bulk/boundary Hilbert spaces. Our result makes extensive use of chord diagram techniques and identifies the Krylov basis of the boundary quantum system with fixed chord number states building the bulk gravitational Hilbert space.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP08(2023)213</doi><tpages>53</tpages><orcidid>https://orcid.org/0000-0003-2248-6913</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | 2D Gravity AdS-CFT Correspondence Black Holes Boundary maps Classical and Quantum Gravitation Complexity Eigenvectors Elementary Particles Field Theories in Lower Dimensions Gravitation theory High energy physics Hilbert space Operators (mathematics) Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Quantum theory Regular Article - Theoretical Physics Relativity Theory String Theory |
| title | A bulk manifestation of Krylov complexity |
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