Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
arXiv:2506.03273 · doi:10.1103/6bgg-vglp
Abstract
Motivated by bulk reconstruction of smeared boundary operators, we study the Krylov complexity of local and non-local primary CFT operators from the local bulk-to-bulk propagator of a minimally-coupled massive scalar field in Rindler-AdS space. We derive analytic and numerical evidence on how the degree of non-locality in the dual CFT 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 space. Our results also show that the evolution of the growth rate of Krylov operator complexity in the CFT 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.
v3: 62 pgs, 25 figures. Matches published version in PRD
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