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arXiv · 2205.01150

Complexity via Replica Trick

Mohsen Alishahiha·Souvik Banerjee·Joshua Kames-King
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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.

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Mohsen Alishahiha, Souvik Banerjee, Joshua Kames-King. 2022-05-02. Complexity via Replica Trick. https://doi.org/10.1007/jhep08(2022)181

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