Timelike entanglement entropy in dS(3)/CFT2

In the context of dS3/CFT2, 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 dS3. The counterpart of this entanglement entropy in AdS(3 )is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS(3). As a result, in both AdS(3)/CFT2 and dS(3)/CFT2, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.

Automated summary

In the context of dS3/CFT2, a timelike entanglement entropy defined by the renormalization group flow is proposed and found to match exactly with the length of a timelike geodesic in dS3. The counterpart of this timelike entanglement entropy in AdS(3) is a spacelike one that extends into the bulk of AdS(3). This discovery indicates the existence of precisely three entanglement entropies in both AdS(3)/CFT2 and dS(3)/CFT2, providing sufficient information to reconstruct the three-dimensional bulk geometry.