Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model
Abstract How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3]...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-10-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP10(2024)107 |
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| author | Sergio E. Aguilar-Gutierrez |
| author_facet | Sergio E. Aguilar-Gutierrez |
| author_sort | Sergio E. Aguilar-Gutierrez |
| collection | DOAJ |
| description | Abstract How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations. |
| format | Article |
| id | doaj-art-b0b890fd962e4d3abb42d07e24c308d1 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-b0b890fd962e4d3abb42d07e24c308d12025-08-20T02:20:44ZengSpringerOpenJournal of High Energy Physics1029-84792024-10-0120241014710.1007/JHEP10(2024)107Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev modelSergio E. Aguilar-Gutierrez0Institute for Theoretical Physics, KU LeuvenAbstract How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS2) field theory/ 3D Schwarzschild de Sitter (SdS3) space in [1–3], we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS3 space, and a boundary time difference of the dual LdS2 CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS2 model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS3 space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS3 space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.https://doi.org/10.1007/JHEP10(2024)107Cosmological modelsde Sitter spaceModels of Quantum Gravity |
| spellingShingle | Sergio E. Aguilar-Gutierrez Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model Journal of High Energy Physics Cosmological models de Sitter space Models of Quantum Gravity |
| title | Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model |
| title_full | Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model |
| title_fullStr | Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model |
| title_full_unstemmed | Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model |
| title_short | Towards complexity in de Sitter space from the doubled-scaled Sachdev-Ye-Kitaev model |
| title_sort | towards complexity in de sitter space from the doubled scaled sachdev ye kitaev model |
| topic | Cosmological models de Sitter space Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP10(2024)107 |
| work_keys_str_mv | AT sergioeaguilargutierrez towardscomplexityindesitterspacefromthedoubledscaledsachdevyekitaevmodel |