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

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.

preprint2020arXivOpen access
Roberto AuzziStefano BaigueraAndrea LegramandiGiuseppe NardelliPratim RoyNicolo Zenoni
hep-th
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Roberto AuzziStefano BaigueraAndrea LegramandiGiuseppe NardelliPratim RoyNicolo Zenoni

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