Krylov spread complexity as holographic complexity beyond JT gravity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908584582840320 |
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| author | Heller, Michal P. Papalini, Jacopo Schuhmann, Tim |
| author_facet | Heller, Michal P. Papalini, Jacopo Schuhmann, Tim |
| contents | One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at infinite temperature and the complexity = volume proposal in classical JT gravity. Our work utilizes the recent connection between double-scaled SYK and sine-dilaton gravity to show that the quantitative relation between Krylov spread complexity and complexity = volume extends to finite temperatures and to full quantum regime on the gravity side at disk level. From the latter we isolate the first quantum correction to the complexity = volume proposal and propose to view it as a complexity of quantum fields in the bulk. Finally, we comment on the switchback effect, whose presence would make the Krylov spread complexity a fully fledged holographic complexity at least in sine-dilaton gravity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17785 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Krylov spread complexity as holographic complexity beyond JT gravity Heller, Michal P. Papalini, Jacopo Schuhmann, Tim High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at infinite temperature and the complexity = volume proposal in classical JT gravity. Our work utilizes the recent connection between double-scaled SYK and sine-dilaton gravity to show that the quantitative relation between Krylov spread complexity and complexity = volume extends to finite temperatures and to full quantum regime on the gravity side at disk level. From the latter we isolate the first quantum correction to the complexity = volume proposal and propose to view it as a complexity of quantum fields in the bulk. Finally, we comment on the switchback effect, whose presence would make the Krylov spread complexity a fully fledged holographic complexity at least in sine-dilaton gravity. |
| title | Krylov spread complexity as holographic complexity beyond JT gravity |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2412.17785 |