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Main Authors: Aguilar-Gutierrez, Sergio E., Camargo, Hugo A., Jahnke, Viktor, Kim, Keun-Young, Nishida, Mitsuhiro
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2506.03273
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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