Tunneling through an Eternal Traversable Wormhole

TL;DR

This paper investigates tunneling spectroscopy in the Maldacena-Qi model, revealing oscillatory signatures that indicate the presence of an eternal traversable wormhole and its underlying symmetries, with results matching bulk and boundary calculations.

Contribution

It provides the first analysis of tunneling spectroscopy as an experimental signature of an eternal traversable wormhole in the Maldacena-Qi model.

Findings

Oscillations in tunneling probability and conductance in the wormhole phase

Signature of SL(2) symmetry in the bulk geometry

Matching bulk and boundary theoretical results

Abstract

The Maldacena-Qi model describes two copies of the Sachdev-Ye-Kitaev model coupled with an additional coupling, and is dual to the Jackiw-Teitelboim gravity which exhibits an eternal traversable wormhole in the low-temperature limit. In this work, we study an experimental consequence of the existence of the traversable wormhole by considering the tunneling spectroscopy for the Maldacena-Qi model. Comparing to the high-temperature black hole phase where the bulk geometry is disconnected, we find that both the tunneling probability and the differential conductance in the low-temperature wormhole phase show non-trivial oscillation, which directly provides an unambiguous signature of the underlying $\operatorname{SL}(2)$ symmetry of the bulk geometry. We also perform bulk calculations in both high and low-temperature phases, which match the results from the boundary quantum theory.