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.

arXiv commentCorrected 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

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Cited by in corpus (23)

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• Time-like Entanglement Entropy in AdS/BCFT
• SVD Entanglement Entropy
• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• Entanglement Phase Transition in Holographic Pseudo Entropy
• There and Back Again: Mapping and Factorising Cosmological Observables
• Bulk reconstruction using timelike entanglement in (A)dS
• Massless Lifshitz Field Theory for Arbitrary $z$
• Pseudo entropy under joining local quenches
• Holographic Timelike Entanglement Entropy from Rindler Method
• Relation between time- and spacelike entanglement entropy
• Sum rule for the pseudo-Rényi entropy
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Duality of Ryu-Takayanagi surfaces inside and outside the horizon
• Field theory aspects of $\eta$-deformed superstring background
• Timelike entanglement and central charge for quantum BTZ black holes
• Detecting quantum chaos via pseudo-entropy
• Holographic timelike entanglement and $c$ theorem for supersymmetric QFTs in ($0+1$)d
• Symmetry Properties of Quantum Dynamical Entropy
• Constraints from Entanglement Wedge Nesting for Holography at a Finite Cutoff
• Holographic timelike entanglement and subregion complexity with scalar hair