Traversable AdS Wormhole via Non-local Double Trace or Janus Deformation

Abstract

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 $T\overline{T}$ 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.

Figures (16)

• Figure 1: A simple construction of traversable AdS wormhole defined by (\ref{['adSwm']}) and (\ref{['WHR']}).
• Figure 2: Plots of $\langle \mathcal{O}_1\mathcal{O}_2\rangle$ for $d=2$. The left graph shows $\langle \mathcal{O}_1\mathcal{O}_2\rangle$ as a function of $k$ at $\nu=\frac{1}{2}$. The middle one does $\langle \mathcal{O}_1\mathcal{O}_2\rangle$ as a function of $z_0$ at $\nu=\frac{1}{2}$. The right one does $\langle \mathcal{O}_1\mathcal{O}_2\rangle$ as a function of $\nu$ for various values of $k$ at $z_0=10$.
• Figure 3: Geodesics in the traversable AdS wormhole. The geodesic curves show the phase transition at $l=2z_0$, where $l$ is the size of the interval $l=|x_a-x_b|$.
• Figure 4: EE with two symmetric regions in different side. Phase $X$ and $Y$ corresponds to $l<z_0$ and $l>z_0$.
• Figure 5: EE with two regions in different side