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.
Auzzi, R., Baiguera, S., Legramandi, A., Nardelli, G., Roy, P., Zenoni, N. (2020). On subregion action complexity in AdS_3 and in the BTZ black hole. JOURNAL OF HIGH ENERGY PHYSICS, 2020(1) [10.1007/JHEP01(2020)066].
On subregion action complexity in AdS_3 and in the BTZ black hole
Baiguera, S;Legramandi, A;
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 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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