Modular Flow and Holographic Timelike Entanglement Entropy in AdS and Flat Holography
Abstract
Timelike entanglement entropy provides a useful probe of holographic theoris, yet an explicit bulk realization of the modular flow underlying its timelike extremal curve construction has so far been lacking. We construct modular flows associated with spacelike and timelike intervals in AdS3/CFT2 and extend this framework to flat3/CCFT2. Beginning with the boundary symmetry generators, we explicitly derive the boundary modular flows and extend them into the bulk, providing a systematic procedure that relates bulk modular flows to the extremal curves and holographic (timelike) entanglement entropy. For spacelike intervals, the resulting bulk modular flows determine the extremal curves, whose integrated line elements reproduce the standard holographic entanglement entropy. We then generalize this approach to timelike intervals, explicitly constructing the modular flows whose fixed points reproduce the extremal spacelike and timelike curves which gives the holographic timelike entanglement entropy. To the best of our knowledge, this is the first explicit construction of the modular flow associated with a timelike extremal curve for a timelike interval. The same procedure is then carried over to flat3/CCFT2, which give rise to the holographic (timelike) entanglement entropy. Finally, we show that the flat space results obtained in this work can be recovered from their AdS3 counterparts in the flat space limit.
Related
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- Entanglement entropy in holographic CFTs with generic boundaries
- Testing holographic computation of entanglement pseudo-entropy in dS3/ICFT2
- Black Hole Entropy and Holographic Entanglement Entropy in DGP Brane Gravity
BibTeX
@misc{shalamzari2026modular,
title = {{Modular Flow and Holographic Timelike Entanglement Entropy in AdS and Flat Holography}},
author = {Mehdi Hakami Shalamzari and Zahra Paygozar and Mahdi Kord Zangeneh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17165},
eprint = {2610.17165},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17165},
}
RIS
TY - UNPB
TI - Modular Flow and Holographic Timelike Entanglement Entropy in AdS and Flat Holography
AU - Mehdi Hakami Shalamzari
AU - Zahra Paygozar
AU - Mahdi Kord Zangeneh
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17165
UR - https://arxiv.org/abs/2610.17165
AB - Timelike entanglement entropy provides a useful probe of holographic theoris, yet an explicit bulk realization of the modular flow underlying its timelike extremal curve construction has so far been lacking. We construct modular flows associated with spacelike and timelike intervals in AdS_3/CFT_2 and extend this framework to flat_3/CCFT_2. Beginning with the boundary symmetry generators, we explicitly derive the boundary modular flows and extend them into the bulk, providing a systematic procedure that relates bulk modular flows to the extremal curves and holographic (timelike) entanglement entropy. For spacelike intervals, the resulting bulk modular flows determine the extremal curves, whose integrated line elements reproduce the standard holographic entanglement entropy. We then generalize this approach to timelike intervals, explicitly constructing the modular flows whose fixed points reproduce the extremal spacelike and timelike curves which gives the holographic timelike entanglement entropy. To the best of our knowledge, this is the first explicit construction of the modular flow associated with a timelike extremal curve for a timelike interval. The same procedure is then carried over to flat_3/CCFT_2, which give rise to the holographic (timelike) entanglement entropy. Finally, we show that the flat space results obtained in this work can be recovered from their AdS_3 counterparts in the flat space limit.
ER -