Geometric interpretation of timelike entanglement entropy

• URL: http://arxiv.org/abs/2408.15752v1
• Date: Wed, 28 Aug 2024 12:36:34 GMT
• Title: Geometric interpretation of timelike entanglement entropy
• Authors: Michal P. Heller, Fabio Ori, Alexandre Serantes,
• Abstract summary: Analytic continuations of holographic entanglement entropy in which the boundary subregion extends along a timelike direction have brought a promise of a novel, time-centric probe of spacetime. We propose that the bulk carriers of this holographic timelike entanglement entropy are boundary-anchored extremal surfaces probing analytic continuation of holographic spacetimes into complex coordinates.
• Score: 44.99833362998488
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Analytic continuations of holographic entanglement entropy in which the boundary subregion extends along a timelike direction have brought a promise of a novel, time-centric probe of the emergence of spacetime. We propose that the bulk carriers of this holographic timelike entanglement entropy are boundary-anchored extremal surfaces probing analytic continuation of holographic spacetimes into complex coordinates. This proposal not only provides a geometric interpretation of all the known cases obtained by direct analytic continuation of closed-form expressions of holographic entanglement entropy of a strip subregion but crucially also opens a window to study holographic timelike entanglement entropy in full generality. We initialize the investigation of complex extremal surfaces anchored on a timelike strip at the boundary of anti-de Sitter black branes. We find multiple complex extremal surfaces and discuss possible principles singling out the physical contribution.

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