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On subregion action complexity in AdS$_3$ and in the BTZ black hole

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arxiv 1910.00526 v2 pith:IA4I7XQX submitted 2019-10-01 hep-th

Roberto Auzzi , Stefano Baiguera , Andrea Legramandi , Giuseppe Nardelli , Pratim Roy , Nicolo Zenoni This is my paper · ORCID
classification hep-th
keywords complexitysubregionactiontermblackfiniteholeproportional
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abstract

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.

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