We analytically compute subsystem action complexity for a segment in the BTZ black hole background up to the finite term, and we find that it is equal to the sum of a linearly divergent term proportional to the size of the subregion and of a term proportional to the entanglement entropy. This elegant structure does not survive to more complicated geometries: in the case of a two segments subregion in AdS$_3$, complexity has additional finite contributions. We give analytic results for the mutual action complexity of a two segments subregion.

中文翻译：

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关于 AdS3 和 BTZ 黑洞中的子区域动作复杂性

我们分析计算 BTZ 黑洞背景中一段的子系统动作复杂度直到有限项，我们发现它等于与子区域大小成正比的线性发散项和与纠缠熵。这种优雅的结构无法在更复杂的几何形状中幸存下来：在 AdS$_3$ 中的两段子区域的情况下，复杂性具有额外的有限贡献。我们给出了两个段子区域的相互作用复杂性的分析结果。