Wormholes, geons, and the illusion of the tensor product

TL;DR

This paper challenges the assumption that the Hilbert space of a holographic wormhole factorizes into boundary parts, revealing that non-factorization leads to unique quantum features and affects correlation functions.

Contribution

It provides a general argument and concrete examples demonstrating that the Hilbert space of a holographic wormhole does not factorize, impacting our understanding of boundary dualities.

Findings

Hilbert space of wormholes does not factorize into boundary Hilbert spaces

Non-factorization explains peculiar features like null states and entanglement

Correlation functions reflect non-factorization effects

Abstract

In this paper I argue that the Hilbert space of states of a holographic, traversable wormhole does not factorize into the tensor product of the boundary Hilbert spaces. After presenting the general argument I analyze two examples: the scalar sectors of the BTZ geon and the AdS$_2$ eternal wormhole. Utilizing real-time holography I derive the Hilbert spaces, identify the dual states and evaluate correlation functions. I show that the number of peculiarities associated with the wormhole and black hole physics emerges once the factorization is \textit{a priori} assumed. This includes null states and null operators, highly entangled vacuum states and the cross-boundary interactions all emerging as avatars of non-factorization.