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.
Auzzi, R., Baiguera, S., Legramandi, A., Nardelli, G., Roy, P., Zenoni, N., On subregion action complexity in AdS3 and in the BTZ black hole, <<JOURNAL OF HIGH ENERGY PHYSICS>>, 2020; (2001): 0-31. [doi:10.1007/JHEP01(2020)066] [http://hdl.handle.net/10807/146064]
On subregion action complexity in AdS3 and in the BTZ black hole
Auzzi, Roberto;Baiguera, Stefano;Nardelli, Giuseppe;Zenoni, Nicolo'
2020
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.
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