Can one hear the shape of a wormhole?

TL;DR

This paper investigates how the geometry of traversable wormholes in AdS space influences the dual 3D holographic CFTs, providing methods to reconstruct wormhole features from boundary entanglement and correlation data.

Contribution

It introduces explicit algorithms to reconstruct the wormhole's scale factor from entanglement entropies and two-point functions, linking bulk geometry to boundary spectral data.

Findings

Wormhole geometry affects the spectrum and entanglement in the dual CFTs.

Algorithms enable reconstruction of the wormhole scale factor from boundary data.

The problem reduces to a Schrödinger inverse spectral problem.

Abstract

A large class of flat big bang - big crunch cosmologies with negative cosmological constant are related by analytic continuation to asymptotically AdS traversable wormholes with planar cross section. In recent works (arXiv: 2102.05057, 2203.11220) it was suggested that such wormhole geometries may be dual to a pair of 3D holographic CFTs coupled via auxiliary degrees of freedom to give a theory that confines in the infrared. In this paper, we explore signatures of the presence of such a wormhole in the state of the coupled pair of 3D theories. We explain how the wormhole geometry is reflected in the spectrum of the confining theory and the behavior of two-point functions and entanglement entropies. We provide explicit algorithms to reconstruct the wormhole scale factor (which uniquely determines its geometry) from entanglement entropies, heavy operator two-point functions, or light operator two-point functions (which contain the spectrum information). In the last case, the physics of the bulk scalar field dual to the light operator is closely related to the quantum mechanics of a one-dimensional particle in a potential derived from the scale factor, and the problem of reconstructing the scale factor from the two-point function is directly related to the problem of reconstructing this Schr\"odinger potential from its spectrum.