Complexity via Replica Trick

Abstract

We consider the complexity of a single-sided AdS black hole as modelled by an end-of-the-world brane. In addition, we present multi-boundary partition functions and matter correlation functions for such a setting. We compute the complexity using a modified replica trick corresponding to the "quenched geodesic length" in JT gravity. The late-time behaviour of complexity shows a saturation to a constant value of order $e^{S_0}$ following a period of linear growth. Furthermore, we show that our approach leads to an improved result for the variance of complexity, namely it being time-independent at late times. We conclude by commenting on the introduction of dynamical end-of-the-world branes.

arXiv comment29 pages, 6 figures

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• A universal approach to Krylov State and Operator complexities
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• On the saturation of late-time growth of complexity in supersymmetric JT gravity
• Encoded information of mixed correlations: the views from one dimension higher