Traversable AdS wormhole via non-local double trace or Janus deformation

A bstract We study (i) Janus deformations and (ii) non-local double trace deformations of a pair of CFTs, as two different ways to construct CFT duals of traversable AdS wormholes. First we construct a simple model of traversable wormholes by gluing two Poincaré AdS geometries and BTZ black holes and compute holographic two point functions and (pseudo) entanglement entropy. We point out that a Janus gravity solution describes a traversable wormhole when the deformation parameter takes imaginary values. On the other hand, we show that double trace deformations between two decoupled CFTs can reproduce two point functions of traversable AdS wormholes. By considering the case where the double trace deformation is given by a non-local $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation, we analyze the dual gravity which implies emergence of wormholes. We present toy model of these deformed CFTs by using free scalars and obtain qualitative behaviors expected for them. We argue that the crucial difference between the two constructions is that a global time slice of wormhole is described by a pure state for Janus deformations, while it is a mixed state for the double trace deformations.