In this work we use the modified replica trick, proposed in arXiv:2205.01150, to compute the late time behaviour of complexity for JT gravity with ${\cal N} = 1$ and ${\cal N} = 2$ supersymmetries. For the ${\cal N} = 1$ theory, we compute the late time behaviour of complexity defined by the ``quenched geodesic length" and obtain the expected saturation of complexity at time $t \sim e^{S_0}$, to a constant value with time-independent variance. For the ${\cal N} = 2$ theory, we explicitly compute complexity at the disk level which yields the late-time linear growth of complexity. However, we comment on the expectation of the late-time saturation by speculating the trumpet partition function and the non-perturbative corrections to the spectral correlation, relevant for the late-time behaviour of complexity. Furthermore, we compute the matter correlation functions for both the theories.
Quantum chaos and late-time equipartition of symmetry-resolved Krylov complexity
Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Instituto de Física Teórica UAM/CSIC（马德里自治大学/西班牙国家科学研究委员会理论物理研究所）；Universidad Autónoma de Madrid（马德里自治大学）
Codimension-Zero Holographic Complexity and Spectral Three-Point Correlators
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Department of Physics, Nagoya University（名古屋大学物理学系）
Quantum complexity and localization in random and time-periodic unitary circuits
Perimeter Institute for Theoretical Physics（Perimeter理论物理研究所）；University of Waterloo（滑铁卢大学）；Indian Institute of Sciences（印度科学学院）；University of Bristol（布里斯托大学）；Jagiellonian University（亚捷隆大学）；Indian Institute of Science（印度科学学院）
