Composite AdS geodesics for CFT correlators and timelike entanglement entropy

TL;DR

This paper develops a method to reconstruct timelike worldlines in AdS from CFT data using composite geodesics, matching correlator-derived lengths and extending to entanglement entropy calculations.

Contribution

It introduces a bulk extremization procedure for composite geodesics connecting timelike-separated boundary points, advancing holographic reconstruction techniques.

Findings

Matching geodesic lengths with CFT correlators in various AdS backgrounds

Agreement of the method in Poincaré, global AdS, and BTZ black hole spacetimes

Refinement of timelike entanglement entropy calculations in AdS3/CFT2

Abstract

We study how to recover timelike worldlines in AdS from CFT data as a toy model for holographically reconstructing realistic observers. We give a bulk extremization procedure that determines composite timelike-spacelike geodesics that connect timelike-separated boundary points. The total geodesic length matches the length extracted from CFT correlators at the timelike-separated points. We show agreement in Poincar\'e AdS, for generic boundary points in global AdS, and also for the BTZ solution, in which the timelike segment probes behind the horizon. We refine related methods to compute timelike entanglement entropy in AdS$_3$/CFT$_2$ and recover known results.