TY - JOUR
T1 - Krylov complexity in conformal field theory
AU - Dymarsky, Anatoly
AU - Smolkin, Michael
N1 - Publisher Copyright:
© 2021 Published by the American Physical Society
PY - 2021/10/15
Y1 - 2021/10/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85116335247&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.104.L081702
DO - 10.1103/PhysRevD.104.L081702
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AN - SCOPUS:85116335247
SN - 2470-0010
VL - 104
JO - Physical Review D
JF - Physical Review D
IS - 8
M1 - L081702
ER -