Traversable Wormhole in AdS and Entanglement

A traversable wormhole generally violates the averaged null energy condition, usually requiring exotic matter. Recently, it has been found that the traversable wormhole can be realized by non-exotic matter in Einstein-Dirac-Maxwell theories in flat space. This paper generalizes discussions to the AdS spacetime and finds traversable wormholes with spherical and planar topologies. Furthermore, based on the AdS/CFT correspondence, we compute the entanglement entropy of strips and disks on two AdS boundaries of the wormhole. We find that entanglement entropy undergoes a phase transition as the subsystem size increases.