Krylov complexity in conformal field theory

Anatoly Dymarsky, Michael Smolkin

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.

Original languageEnglish
Article numberL081702
JournalPhysical Review D
Issue number8
StatePublished - Oct 15 2021

Bibliographical note

Funding Information:
United States-Israel Binational Science Foundation

Funding Information:
We thank Alex Avdoshkin, Paweł Caputa, Mark Mezei and Alexander Zhiboedov for discussions. This work is supported by the United States-Israel BSF Grant No. 2016186.

Publisher Copyright:
© 2021 Published by the American Physical Society

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


Dive into the research topics of 'Krylov complexity in conformal field theory'. Together they form a unique fingerprint.

Cite this