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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 Ã°ï¿½?Â© = 1 and Ã°ï¿½?Â© = 2 supersymmetries. For the Ã°ï¿½?Â© = 1 theory, we compute the late time behaviour of complexity defined by the Ã¢??quenched geodesic lengthÃ¢?ï¿½ and obtain the expected saturation of complexity at time tÃ¢?Â¼eS0, to a constant value with time-independent variance. For the Ã°ï¿½?Â© = 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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