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arXiv · 2108.08308

Product of Random States and Spatial (Half-)Wormholes

Kanato Goto·Yuya Kusuki·Kotaro Tamaoka·Tomonori Ugajin
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Abstract

We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry. It has been shown, quantum entanglement plays a key role in the emergence of such a geometric structure, namely a smooth Einstein-Rosen bridge. In this paper, we explore the possibility of the emergence of similar geometric structure from classical correlation, in the AdS/CFT setup. To this end, we consider a setup where we have two decoupled CFT Hilbert spaces, then choose a random typical state in one of the Hilbert spaces and the same state in the other. The total state in the fine-grained picture is of course a tensor product state, but averaging over the states sharing the same random coefficients creates a geometric connection for simple probes. Then, the apparent spatial wormhole causes a factorization puzzle. We argue that there is a spatial analog of half-wormholes, which resolves the puzzle in the similar way as the spacetime half-wormholes.

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Kanato Goto, Yuya Kusuki, Kotaro Tamaoka, Tomonori Ugajin. 2021-08-18. Product of Random States and Spatial (Half-)Wormholes. https://doi.org/10.1007/jhep10(2021)205

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