A bulk manifestation of Krylov complexity Article Swipe
Eliezer Rabinovici
,
A. Sánchez-Garrido
,
Ruth Shir
,
Julian Sonner
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/jhep08(2023)213
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/jhep08(2023)213
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.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/jhep08(2023)213
- https://link.springer.com/content/pdf/10.1007/JHEP08(2023)213.pdf
- OA Status
- diamond
- Cited By
- 72
- References
- 50
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4386314537
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https://doi.org/10.1007/jhep08(2023)213Digital Object Identifier
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A bulk manifestation of Krylov complexityWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
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2023-08-31Full publication date if available
- Authors
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Eliezer Rabinovici, A. Sánchez-Garrido, Ruth Shir, Julian SonnerList of authors in order
- Landing page
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https://doi.org/10.1007/jhep08(2023)213Publisher landing page
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https://link.springer.com/content/pdf/10.1007/JHEP08(2023)213.pdfDirect link to full text PDF
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diamondOpen access status per OpenAlex
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https://link.springer.com/content/pdf/10.1007/JHEP08(2023)213.pdfDirect OA link when available
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Physics, Hilbert space, Quantum gravity, Boundary (topology), Gravitation, Theoretical physics, Mutually unbiased bases, Quantum mechanics, Quantum, Mathematics, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
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72Total citation count in OpenAlex
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2025: 36, 2024: 22, 2023: 14Per-year citation counts (last 5 years)
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| referenced_works | https://openalex.org/W4249956767, https://openalex.org/W1889142700, https://openalex.org/W2117187503, https://openalex.org/W2014489580, https://openalex.org/W2203723895, https://openalex.org/W3172713805, https://openalex.org/W2904845127, https://openalex.org/W2960588259, https://openalex.org/W3083018415, https://openalex.org/W4224215230, https://openalex.org/W2175998061, https://openalex.org/W2092581607, https://openalex.org/W3081039832, https://openalex.org/W3172241679, https://openalex.org/W2900051186, https://openalex.org/W2808052156, https://openalex.org/W3007873191, https://openalex.org/W4309082140, https://openalex.org/W2007833526, https://openalex.org/W2252917783, https://openalex.org/W2344612405, https://openalex.org/W2581653392, https://openalex.org/W2032520835, https://openalex.org/W3189118613, https://openalex.org/W3101198211, https://openalex.org/W2415090955, https://openalex.org/W2047749712, https://openalex.org/W4251340380, https://openalex.org/W2468247974, https://openalex.org/W3001297680, https://openalex.org/W2588723549, https://openalex.org/W4206175892, https://openalex.org/W2076870783, https://openalex.org/W2770694769, https://openalex.org/W2060083150, https://openalex.org/W2154320483, https://openalex.org/W3047239568, https://openalex.org/W4385714694, https://openalex.org/W3165288519, https://openalex.org/W3178119464, https://openalex.org/W4233172436, https://openalex.org/W3203968734, https://openalex.org/W4378904582, https://openalex.org/W3102226719, https://openalex.org/W3124113507, https://openalex.org/W3201218626, https://openalex.org/W3134594783, https://openalex.org/W3124875895, https://openalex.org/W3101529462, https://openalex.org/W3102564242 |
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| corresponding_author_ids | https://openalex.org/A5088050489 |
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