Product of random states and spatial (half-)wormholes
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.
Additional Information
© 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: September 14, 2021; Accepted: October 5, 2021; Published: October 26, 2021. We thank Yasunori Nomura, Masahiro Nozaki, Kenta Suzuki, Tadashi Takayanagi, and Zixia Wei for useful discussion. KG is supported by JSPS Grant-in-Aid for Early-Career Scientists 21K13930. KT is supported by JSPS Grant-in-Aid for Early-Career Scientists 21K13920. TU is supported by JSPS Grant-in-Aid for Young Scientists 19K14716. YK is supported by RIKEN iTHEMS Program, and the RIKEN Special Postdoctoral Researcher program.Attached Files
Published - Goto2021_Article_ProductOfRandomStatesAndSpatia.pdf
Accepted Version - 2108.08308.pdf
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Additional details
- Eprint ID
- 112047
- Resolver ID
- CaltechAUTHORS:20211124-183511245
- 21K13930
- Japan Society for the Promotion of Science (JSPS)
- 21K13920
- Japan Society for the Promotion of Science (JSPS)
- 19K14716
- Japan Society for the Promotion of Science (JSPS)
- RIKEN
- SCOAP3
- Created
-
2021-11-24Created from EPrint's datestamp field
- Updated
-
2021-11-24Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics