Timelike entanglement entropy in dS3/CFT2

Abstract

A bstract In the context of dS 3 /CFT 2 , 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 3 . 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 /CFT 2 and dS 3 /CFT 2 , there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.