Understand
We study the entanglement entropy for time-like subsystem in two-dimensional boundary conformal field theory (BCFT) both from the field theory and holographic point of view.
- In field theory, we compute the time-like entanglement entropy of a pure time-like interval at zero and finite temperature using the replica technique and analytical continuation.
- We find that, similar to the ordinary space-like entanglement entropy in BCFT, the time-like entropy also has a bulk phase and a boundary phase which corresponds respectively to the dominance of the identity block in the bulk and boundary OPE channels.
- However, we find that in Lorentzian BCFT, the time-like entanglement entropy posses a third {\it Regge phase} which arises in the Regge limit of the interval, when one endpoint of the time interval approaches the light cone of the mirror image of the other endpoint.