On subregion action complexity in AdS3 and in the BTZ black hole

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 AdS3, complexity has additional finite contributions. We give analytic results for the mutual action complexity of a two segments subregion.

A preprint version of the article is available at ArXiv.

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Auzzi, R., Baiguera, S., Legramandi, A. et al. On subregion action complexity in AdS3 and in the BTZ black hole. J. High Energ. Phys. 2020, 66 (2020). https://doi.org/10.1007/JHEP01(2020)066

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Keywords

  • AdS-CFT Correspondence
  • Black Holes