Krylov complexity in quantum field theory, and beyond

Alexander Avdoshkin, Anatoly Dymarsky*, Michael Smolkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.

Original languageEnglish
Article number66
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.


  • AdS-CFT Correspondence
  • Effective Field Theories
  • Nonperturbative Effects


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