Complexity via Replica Trick

TL;DR

This paper investigates the complexity of single-sided AdS black holes modeled by end-of-the-world branes, using a modified replica trick in JT gravity to analyze late-time behavior and variance of complexity.

Contribution

It introduces a novel approach to compute complexity via a modified replica trick and provides new insights into late-time saturation and variance of complexity in black hole models.

Findings

Complexity saturates to a constant of order e^{S_0} after linear growth.

Late-time variance of complexity is time-independent and improved.

Provides multi-boundary partition functions and matter correlation functions in this setting.

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.