Krylov complexity in conformal field theory

Understand

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.