On the saturation of late-time growth of complexity in supersymmetric JT gravity

Abstract

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 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 ~ e S 0 $$ t\sim {e}^{S_0} $$ , 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.

Keywords

• 2D Gravity
• AdS-CFT Correspondence
• Matrix Models