2025/06/03 by Sergio E. Aguilar-Gutierrez, Hugo A. Camargo, Aguilar-Gutierrez, Sergio E. +7 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2506.03273
openalex publication_date 2025/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFTd operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in Rindler-AdSd+1 space. We derive analytic and numerical evidence on how the degree of non-locality in the dual CFTd 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 AdSd+1 space. Our results also show that the evolution of the growth rate of Krylov operator complexity in the CFTd 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.