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

TL;DR

This paper explores two methods—Janus and non-local double trace deformations—to construct and analyze traversable AdS wormholes, revealing their holographic duals, entanglement properties, and the nature of the states involved.

Contribution

It introduces a simple model for traversable wormholes using gluing of AdS geometries and BTZ black holes, and compares Janus and double trace deformations, highlighting their differences in state purity.

Findings

Janus deformations describe wormholes with pure states.

Double trace deformations lead to mixed states in wormholes.

Non-local Tar{T} deformation induces wormhole emergence in dual gravity.

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 Poincar\'e 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.