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.

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

References in corpus (6)

• Towards a derivation of holographic entanglement entropy
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• Pseudo Entropy in Free Quantum Field Theories
• de Sitter extremal surfaces
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• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
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• Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($0+1$)d
• Symmetry Properties of Quantum Dynamical Entropy
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• Holographic timelike entanglement and subregion complexity with scalar hair