Bulk view of teleportation and traversable wormholes

Abstract

We construct detailed AdS 2 gravity solutions describing the teleportation through a traversable wormhole sending a state from one side of the wormhole to the other. The traversable wormhole is realized by turning on a double trace interaction that couples the two boundaries of an eternal AdS 2 black hole. The horizon radius or the entropy of the black hole is reduced consistently with the boundary computation of the energy change, confirming the black hole first law. To describe teleportee states traveling through the wormhole, we construct Janus deformations which make the Hamiltonians of left-right boundaries differ from each other by turning on exact marginal operators. Combining explicitly the traversable wormhole solution and the teleportee states, we present a complete bulk picture of the teleportation in the context of ER=EPR. The traversability of the wormhole is not lost to the leading order of the deformation parameter. We also consider solutions where the teleportee meets the matter thrown from the other side during teleportation, in accordance with the assertion that the bulk wormhole is experimentally observable.

Experimental probes of traversable wormholes

“…In this section we summarize our bulk construction of black hole/wormhole transition in [19,20]. Our setup is based on two-dimensional Einstein-dilaton gravity, known as the JT model.…”

“…where we used SL(2, R) to set the solution in the above form [19]. Here, the length dimension parameter L could be interpreted as the horizon radius, which can be shown as follows: By an appropriate coordinate transformation the above AdS 2 metric can be set in the form of the black hole metric as…”

“…Here, φ L = φ R can be identified withφ in the bulk and g is a coupling proportional to the parameter h, whose explicit identification is given by [19]…”

“…Though the metric is not affected by the presence of the matter field χ, the deformation (2.11) via the scalar field χ affect the dilaton field φ through (2.4). The general solution of (2.4) can be written as [19] φ = φ hom + ϕ, (2.15) where φ hom denotes a vacuum solution (i.e. T ab = 0 case) and ϕ is given by…”

“…If the bulk starts with the two-sided black hole spacetime, the corresponding boundary system should be prepared at some initial timeũ I (< 0) in a particularly entangled state, more specifically, a so-called thermofield double state. Basically here we are following the general correspondence between the two-sided black hole spacetime and the thermofield double description of the L-R boundary system [26,19]. In this correspondence, the initial state is given by…”