  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.
