TY - JOUR
T1 - Krylov complexity in quantum field theory, and beyond
AU - Avdoshkin, Alexander
AU - Dymarsky, Anatoly
AU - Smolkin, Michael
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/6
Y1 - 2024/6
N2 - We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.
AB - We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.
KW - AdS-CFT Correspondence
KW - Effective Field Theories
KW - Nonperturbative Effects
UR - http://www.scopus.com/inward/record.url?scp=85196172010&partnerID=8YFLogxK
U2 - 10.1007/JHEP06(2024)066
DO - 10.1007/JHEP06(2024)066
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AN - SCOPUS:85196172010
SN - 1126-6708
VL - 2024
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 6
M1 - 66
ER -