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Paper IPM / P / 17174  


Abstract:  
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 timeindependent variance. For the Ã°ï¿½?Â© = 2 theory, we explicitly compute complexity at the disk level which yields the latetime linear growth of complexity. However, we comment on the expectation of the latetime saturation by speculating the trumpet partition function and the nonperturbative 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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