On holographic time-like entanglement entropy
Abstract
In order to study the pseudo entropy of time-like subregions holographically, the previous smooth space-like extremal surface was recently generalized to mix space-like and time-like segments and the area becomes complex value. This paper finds that, if one tries to use such kind of piecewise smooth extremal surfaces to compute time-like entanglement entropy holographically, the complex area is not unique in general. We then generalize the original holographic proposal of space-like entanglement entropy to pick up a unique area from all allowed ``space-like+time-like'' piecewise smooth extremal surfaces for a time-like subregion. We will give some concrete examples to show the correctness of our proposal.
Cite
@article{arxiv.2211.14883,
title = {On holographic time-like entanglement entropy},
author = {Ze Li and Zi-Qing Xiao and Run-Qiu Yang},
journal= {arXiv preprint arXiv:2211.14883},
year = {2023}
}
Comments
Corrected a few typos of figures and main text; Added a brief discussion on the ambiguity of the imaginary part from the choice of branch. Accepted by JHEP