Holographic timelike entanglement in AdS${}_3$ Vaidya

Abstract

Based on the studies of pseudo-entropy in de Sitter, there have been recent proposals for a timelike entanglement in AdS/CFT. In this work, we explore this proposal in the context of a holographic CFT undergoing a global quench. We study various cases in which the timelike intervals are anchored at various boundary times, sometimes straddling the infalling shell. The early and late time behaviours reproduce the known results coming from the pure AdS and the black hole geometry dual to the thermal CFT state respectively. However when the infalling shock straddles the timelike interval, the dynamics drastically differs from how the entanglement entropy evolves.

arXiv commentVersion 1. 27 pages, 17 figures. Version 2. 30 pages. Corrected analysis of case 4 showing approach to thermalization. References and appendices added. Typos corrected. Version 3. 31 pages, 17 figures. Matches published version except an extra note added at the end of the introduction section

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