Abstract
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 AdS3 is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS3. As a result, in both AdS3/CFT2 and dS3/CFT2, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.
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Details
1 Sichuan University, College of Physics, Chengdu, China (GRID:grid.13291.38) (ISNI:0000 0001 0807 1581)
2 Sichuan University, College of Physics, Chengdu, China (GRID:grid.13291.38) (ISNI:0000 0001 0807 1581); University of Cambridge, DAMTP, Centre for Mathematical Sciences, Cambridge, U.K. (GRID:grid.5335.0) (ISNI:0000 0001 2188 5934)