Universal corrections to entanglement entropy of local quantum quenches and scrambling time

We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in 2d CFTs at finite temperature for which the locally excited states have a finite temporal width, \epsilon. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Renyi and entanglement entropies at order \epsilon^2 is universal. It is determined by the expectation value of the stress tensor in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the \epsilon^2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We compute another correction when the CFT has higher spin chemical potential, and find that its time dependence is universal.
We study the mutual information between two regions of the Kruskal extension of BTZ black hole in the presence of an infalling massive particle in the right region. The infalling particle starts its motion at a distance \epsilon from the boundary and falls towards the horizon. We evaluate the correction to scrambling time (time when mutual information vanishes) when the infalling particle has spin-3 charge.