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arXiv · 2211.14883

On holographic time-like entanglement entropy

Ze Li·Zi-Qing Xiao·Run-Qiu Yang
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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.

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Ze Li, Zi-Qing Xiao, Run-Qiu Yang. 2022-11-27. On holographic time-like entanglement entropy. https://doi.org/10.1007/jhep04(2023)004

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