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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.03273 |
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| _version_ | 1866908827059748864 |
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| author | Aguilar-Gutierrez, Sergio E. Camargo, Hugo A. Jahnke, Viktor Kim, Keun-Young Nishida, Mitsuhiro |
| author_facet | Aguilar-Gutierrez, Sergio E. Camargo, Hugo A. Jahnke, Viktor Kim, Keun-Young Nishida, Mitsuhiro |
| contents | Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFT$_d$ operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in Rindler-AdS$_{d+1}$ space. We derive analytic and numerical evidence on how the degree of non-locality in the dual CFT$_d$ observable affects the evolution of Krylov complexity and the Lanczos coefficients. Curiously, the near-horizon limit matches with the same observable for conformally-coupled probe scalar fields inserted at the asymptotic boundary of AdS$_{d+1}$ space. Our results also show that the evolution of the growth rate of Krylov operator complexity in the CFT$_d$ takes the same form as to the proper radial momentum of a probe particle inside the bulk to a good approximation. The exact equality only occurs when the probe particle is inserted in the asymptotic boundary or in the horizon limit. Our results capture a prosperous interplay between Krylov complexity in the CFT, thermal ensembles at finite bulk locations and their role in the holographic dictionary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_03273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum Aguilar-Gutierrez, Sergio E. Camargo, Hugo A. Jahnke, Viktor Kim, Keun-Young Nishida, Mitsuhiro High Energy Physics - Theory Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFT$_d$ operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in Rindler-AdS$_{d+1}$ space. We derive analytic and numerical evidence on how the degree of non-locality in the dual CFT$_d$ observable affects the evolution of Krylov complexity and the Lanczos coefficients. Curiously, the near-horizon limit matches with the same observable for conformally-coupled probe scalar fields inserted at the asymptotic boundary of AdS$_{d+1}$ space. Our results also show that the evolution of the growth rate of Krylov operator complexity in the CFT$_d$ takes the same form as to the proper radial momentum of a probe particle inside the bulk to a good approximation. The exact equality only occurs when the probe particle is inserted in the asymptotic boundary or in the horizon limit. Our results capture a prosperous interplay between Krylov complexity in the CFT, thermal ensembles at finite bulk locations and their role in the holographic dictionary. |
| title | Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.03273 |