Scrambling time from local perturbations of the eternal BTZ black hole

J.L.F. Barbón, Eliezer Rabinovici

Pawel Caputa, Joan Simón, Andrius Štikonas +2 more

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 tω 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 tω . In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.

Andrius Štikonas

Abstract 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.

Ralf Schützhold, William George Unruh

ATHARVA ANUP WASNIK

Andrius Štikonas

In this thesis we study the time evolution of Rényi and entanglement entropies of thermal states in Conformal Field Theory (CFT). These quantities are usually hard to compute but Ryu-Takayanagi (RT) and Hubeny-Rangamani-Takayanagi (HRT) proposals allow us to find the same quantities using calculations in general relativity. We will introduce main concepts of holography, quantum information and conformal field theory that will be used to derive the results of this thesis. In the first part of the thesis, we explicitly compute entanglement entropy of the rotating BTZ black hole by directly applying HRT proposal and finding lengths of spacelike geodesics. Rényi entropy of thermal state perturbed by a local quantum quench is computed by mapping correlators on two glued cylinders to the plane for field theory containing a single free boson and for 2d CFTs in the large c limit. We consider Thermofield Double State (TFD) which is an entangled state in direct product of two 2D CFTs. It is conjectured to be holographically equivalent to the eternal BTZ black hole. TFD state is perturbed by a local quench in one CFT and mutual information between two intervals in two CFTs is computed. We find when mutual information vanishes and interpret this as scrambling time, i.e. time scale required for the system to thermalize. This field theory result is modelled with a massive free falling particle in the BTZ black hole. We have computed the back-reaction of the particle on the metric of BTZ and used RT proposal to find holographic entanglement entropy. Finally, we generalize this calculation to the case of rotating BTZ with inner and outer horizons. It is dual to the CFT with different temperatures for left and right moving modes. We calculate mutual information and scrambling time and find exact agreement between results in the gravity and those in the CFT.