Scrambling time from local perturbations of the eternal BTZ black hole

TL;DR

This paper calculates the scrambling time in a 2d CFT dual to an eternal BTZ black hole, showing how local perturbations destroy entanglement, with results matching holographic shock-wave models.

Contribution

It provides an exact computation of the scrambling time in a 2d CFT after local perturbations, linking field theory results with holographic shock-wave descriptions.

Findings

Mutual information vanishes at the scrambling time.

Holographic description matches CFT calculations.

Results valid for any perturbation time $t_\omega$."

Abstract

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