Abstract
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 language | English |
|---|---|
| Article number | L081702 |
| Journal | Physical Review D |
| Volume | 104 |
| Issue number | 8 |
| DOIs | |
| State | Published - Oct 15 2021 |
Bibliographical note
Publisher Copyright:© 2021 Published by the American Physical Society
Funding
United States-Israel Binational Science Foundation 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.
| Funders | Funder number |
|---|---|
| United States-Israel BSF | 2016186 |
| United States-Israel Binational Science Foundation |
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)