Timelike entanglement entropy in dS$_3$/CFT$_2$
Abstract
In the context of dS/CFT, we propose a timelike entanglement entropy defined by the renormalization group flow. This timelike entanglement entropy is calculated in CFT by using the Callan-Symanzik equation. We find an exact match between this entanglement entropy and the length of a timelike geodesic connecting two different spacelike surfaces in dS.The counterpart of this entanglement entropy in AdS is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS. As a result, in both AdS/CFT and dS/CFT, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.
Cite
@article{arxiv.2304.10376,
title = {Timelike entanglement entropy in dS$_3$/CFT$_2$},
author = {Xin Jiang and Peng Wang and Houwen Wu and Haitang Yang},
journal= {arXiv preprint arXiv:2304.10376},
year = {2024}
}
Comments
v1: 9 pages, 1 figure; v2: references added, fixed typos; v3: matches published version