Diving into booklet wormholes

TL;DR

This paper investigates the geometric and quantum properties of booklet wormholes, revealing unique symmetries and junction conditions, and explores how to make these wormholes traversable through boundary deformations.

Contribution

It extends the study of booklet wormholes by analyzing their junction conditions, symmetries, and traversability, highlighting novel quantum non-local effects and observer-dependent perceptions.

Findings

Bulk symmetries require special Killing vector fields.

Quantum non-local junction conditions are necessary at multi-way interfaces.

Boundary deformations can render wormholes traversable, encoding information in entanglement.

Abstract

ArXiv:2508.17898 proposed the booklet wormhole as the holographic dual of the GHZ state. This paper extends the investigation into this geometry, particularly focusing on the junction conditions for matter fields. We show that the symmetry of the GHZ state requires the bulk to admit special Killing vector fields that standard manifolds cannot realize. Moreover, these bulk symmetries require unprecedented quantum non-local junction conditions at the multi-way interface: Observers entering from different horizons will perceive different states inside the wormhole, where the junction conditions appear as constraints on the observables of different sets of observers. We finally discuss how to render booklet wormholes traversable via boundary deformations. A localized wave packet injected from one page generally evolves into a non-local mixed state on each remaining page, with the information encoded in the entanglement between different pages.