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Paper   IPM / Physic / 17174
School of Physics
  Title:   On the saturation of late-time growth of complexity in supersymmetric JT gravity
1.  M. Alishahiha
2.  S. Banerjee
  Status:   Published
  Journal: JHEP
  Vol.:  2023
  Year:  2023
  Pages:   134
  Supported by:  IPM
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 𝒩 = 1 and 𝒩 = 2 supersymmetries. For the 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∼eS0, to a constant value with time-independent variance. For the 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.

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