2016年3月
Emergent classical geometries on boundaries of randomly connected tensor networks
PHYSICAL REVIEW D
- ,
- ,
- 巻
- 93
- 号
- 6
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevD.93.064071
- 出版者・発行元
- AMER PHYSICAL SOC
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors the dimensions of the spaces can be freely chosen, and the geometries-which are curved in general-can be varied. We give the explicit solvable examples of emergent flat tori in arbitrary dimensions, and the correspondence from the tensors to the geometries for general curved cases. The perturbative dynamics in the emergent space is shown to be described by an effective action which is invariant under the spatial diffeomorphism due to the underlying orthogonal group symmetry of the randomly connected tensor network. It is also shown that there are various phase transitions among spaces, including extended and point-like ones, under continuous change of the tensors.
- リンク情報
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- DOI
- https://doi.org/10.1103/PhysRevD.93.064071
- arXiv
- http://arxiv.org/abs/arXiv:1601.04232
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000373106800003&DestApp=WOS_CPL
- URL
- http://arxiv.org/abs/1601.04232v1
- ID情報
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- DOI : 10.1103/PhysRevD.93.064071
- ISSN : 2470-0010
- eISSN : 2470-0029
- arXiv ID : arXiv:1601.04232
- Web of Science ID : WOS:000373106800003