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.
Highlights
An ensemble of field theories on the boundary, instead of a single field theory
We study how coarse-graining procedure of an underlying UV-complete quantum gravity gives rise to a connected geometry
Spatial wormholes constitute another class of wormholes, and they are distinguished from the spacetime wormholes related to averaging over theories
Summary
We will argue that averaging over states on a bipartite system HL ⊗ HR leads to a correlation between two system, which signals the existence of spatial wormholes connecting these two boundaries. There are several notions of averaging over states or matrix elements that are closely related but different in detail. We would like to figure out precisely which state averaging leads to a realistic wormhole structure in the bulk. The purpose of this section is to review these notions and clarify the differences among them
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