Product of Random States and Spatial (Half-)Wormholes

TL;DR

This paper investigates how classical correlations in a dual CFT setup can give rise to geometric structures akin to wormholes, highlighting the role of random states and half-wormholes in resolving factorization puzzles.

Contribution

It introduces a novel classical correlation mechanism for wormhole emergence in AdS/CFT, paralleling quantum entanglement effects and proposing a spatial half-wormhole concept.

Findings

Classical correlations can produce geometric connections similar to wormholes.

Averaging over random states creates effective spacetime bridges.

Spatial half-wormholes resolve factorization puzzles in the model.

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.