The bulk Hilbert space of double scaled SYK
Abstract The emergence of the bulk Hilbert space is a mysterious concept in holography. In [1], the SYK model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert space of double scaled SYK by slicing open these chord diagrams; this Hilbert...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP11(2022)060 |
| _version_ | 1797865757524099072 |
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| author | Henry W. Lin |
| author_facet | Henry W. Lin |
| author_sort | Henry W. Lin |
| collection | DOAJ |
| description | Abstract The emergence of the bulk Hilbert space is a mysterious concept in holography. In [1], the SYK model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert space of double scaled SYK by slicing open these chord diagrams; this Hilbert space resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This bulk reconstruction is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II1 algebra of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical SL(2, ℝ) symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques. |
| first_indexed | 2024-04-09T23:13:22Z |
| format | Article |
| id | doaj.art-aac09a07abbb4d4495e893f16f055ddb |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:22Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-aac09a07abbb4d4495e893f16f055ddb2023-03-22T10:15:33ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221113310.1007/JHEP11(2022)060The bulk Hilbert space of double scaled SYKHenry W. Lin0Institute for Advanced StudyAbstract The emergence of the bulk Hilbert space is a mysterious concept in holography. In [1], the SYK model was solved in the double scaling limit by summing chord diagrams. Here, we explicitly construct the bulk Hilbert space of double scaled SYK by slicing open these chord diagrams; this Hilbert space resembles that of a lattice field theory where the length of the lattice is dynamical and determined by the chord number. Under a calculable bulk-to-boundary map, states of fixed chord number map to particular entangled 2-sided states with a corresponding size. This bulk reconstruction is well-defined even when quantum gravity effects are important. Acting on the double scaled Hilbert space is a Type II1 algebra of observables, which includes the Hamiltonian and matter operators. In the appropriate quantum Schwarzian limit, we also identify the JT gravitational algebra including the physical SL(2, ℝ) symmetry generators, and obtain explicit representations of the algebra using chord diagram techniques.https://doi.org/10.1007/JHEP11(2022)0602D GravityAdS-CFT Correspondence |
| spellingShingle | Henry W. Lin The bulk Hilbert space of double scaled SYK Journal of High Energy Physics 2D Gravity AdS-CFT Correspondence |
| title | The bulk Hilbert space of double scaled SYK |
| title_full | The bulk Hilbert space of double scaled SYK |
| title_fullStr | The bulk Hilbert space of double scaled SYK |
| title_full_unstemmed | The bulk Hilbert space of double scaled SYK |
| title_short | The bulk Hilbert space of double scaled SYK |
| title_sort | bulk hilbert space of double scaled syk |
| topic | 2D Gravity AdS-CFT Correspondence |
| url | https://doi.org/10.1007/JHEP11(2022)060 |
| work_keys_str_mv | AT henrywlin thebulkhilbertspaceofdoublescaledsyk AT henrywlin bulkhilbertspaceofdoublescaledsyk |