Abstract
We study higher-dimensional traversable wormholes in the context of Rindler-AdS/CFT. The hyperbolic slicing of a pure AdS geometry can be thought of as a topological black hole that is dual to a conformal field theory in the hyperbolic space. The maximally extended geometry contains two exterior regions (the Rindler wedges of AdS) which are connected by a wormhole. We show that this wormhole can be made traversable by a double trace deformation that violates the average null energy condition (ANEC) in the bulk. We find an analytic formula for the ANEC violation that generalizes Gao-Jafferis-Wall result to higher-dimensional cases, and we show that the same result can be obtained using the eikonal approximation. We show that the bound on the amount of information that can be transferred through the wormhole quickly reduces as we increase the dimensionality of spacetime. We also compute a two-sided commutator that diagnoses traversability and show that, under certain conditions, the information that is transferred through the wormhole propagates with butterfly speed {upsilon}_B=frac{1}{d-1} .
Highlights
The maximally extended geometry contains two exterior regions which are connected by a wormhole
We find an analytic formula for the average null energy condition (ANEC) violation that generalizes Gao-Jafferis-Wall result to higher-dimensional cases, and we show that the same result can be obtained using the eikonal approximation
We consider the hyperbolic slicing of a pure AdS geometry, which can be thought of as a topological hyperbolic black hole
Summary
We consider a Rindler-AdS solution, which can be constructed as follows. We start with a pure AdSd+1 geometry, which can be defined as the universal cover of the hyperboloid. Each Rindler wedge is described by a CFT living in R × Hd−1 We denote these hyperbolic space CFTs as CFTL and CFTR, where L and R label the left and the right boundary, respectively. The description above shows that a global AdS geometry can be seen as a maximally extended black hole-like geometry, whose boundary description is given in terms of a thermofield double state of two CFTs in hyperbolic space. For a more detailed discussion about subregion duality, we refer to [33]
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