In this paper, we investigate the entanglement entropy of the rotating BTZ black hole perturbed by a massive back-reacting free falling particle. Then, mutual information between two finite intervals in two asymptotic regions of rotating BTZ is derived. It allows us to find the scrambling time, the time scale in which mutual information vanishes. We give a dual large c CFT description in terms of a thermofield double state with different temperatures for left and right moving modes that is perturbed by a local operator. Exact matching between gravity and CFT results is obtained.

United Kingdom

Andrius Štikonas

Scrambling time from local perturbations of the rotating BTZ black hole

We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time t ω in the large c limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time t ω . In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.

Sweden

Pawel Caputa

Joan Simón

Japan

Tadashi Takayanagi

Kento Watanabe

Scrambling time from local perturbations of the eternal BTZ black hole

In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.