A bulk manifestation of Krylov complexity
Abstract 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 K...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2023)213 |
| _version_ | 1797647423378554880 |
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| author | E. Rabinovici A. Sánchez-Garrido R. Shir J. Sonner |
| author_facet | E. Rabinovici A. Sánchez-Garrido R. Shir J. Sonner |
| author_sort | E. Rabinovici |
| collection | DOAJ |
| description | Abstract 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 AdS2. 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 AdS2 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. |
| first_indexed | 2024-03-11T15:17:08Z |
| format | Article |
| id | doaj.art-b427cda9f32d4fe7b23724d237ed99bb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-11T15:17:08Z |
| publishDate | 2023-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b427cda9f32d4fe7b23724d237ed99bb2023-10-29T12:12:38ZengSpringerOpenJournal of High Energy Physics1029-84792023-08-012023815310.1007/JHEP08(2023)213A bulk manifestation of Krylov complexityE. Rabinovici0A. Sánchez-Garrido1R. Shir2J. Sonner3Racah Institute of Physics, The Hebrew UniversityDepartment of Theoretical Physics, University of GenevaDepartment of Physics and Materials Science, University of LuxembourgDepartment of Theoretical Physics, University of GenevaAbstract 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 AdS2. 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 AdS2 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.https://doi.org/10.1007/JHEP08(2023)2132D GravityAdS-CFT CorrespondenceBlack HolesField Theories in Lower Dimensions |
| spellingShingle | E. Rabinovici A. Sánchez-Garrido R. Shir J. Sonner A bulk manifestation of Krylov complexity Journal of High Energy Physics 2D Gravity AdS-CFT Correspondence Black Holes Field Theories in Lower Dimensions |
| title | A bulk manifestation of Krylov complexity |
| title_full | A bulk manifestation of Krylov complexity |
| title_fullStr | A bulk manifestation of Krylov complexity |
| title_full_unstemmed | A bulk manifestation of Krylov complexity |
| title_short | A bulk manifestation of Krylov complexity |
| title_sort | bulk manifestation of krylov complexity |
| topic | 2D Gravity AdS-CFT Correspondence Black Holes Field Theories in Lower Dimensions |
| url | https://doi.org/10.1007/JHEP08(2023)213 |
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