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Wormholes, geons, and the illusion of the tensor product (2212.10652v1)
Published 20 Dec 2022 in hep-th
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.