Holographic duality from random tensor networks
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No Canadian affiliation. An affiliation-only frame — the usual design — would never have seen this work. It is one of the works that make the case for inverting the frame.
Machine scores (provisional)
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- Teacher spread
- 0.201 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main results of the article define a more general form of bulk-boundary correspondence which could be useful for extending holography to other spacetimes.
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The record
- Venue
- Journal of High Energy Physics
- Topic
- Black Holes and Theoretical Physics
- Field
- Physics and Astronomy
- Canadian institutions
- —
- Funders
- Division of Materials ResearchFoundational Questions InstituteCanadian Institute for Advanced ResearchSimons FoundationDavid and Lucile Packard FoundationNational Science Foundation
- Keywords
- Quantum entanglementMultipartite entanglementIsing modelEntropy (arrow of time)Boundary (topology)Duality (order theory)Partition function (quantum field theory)Squashed entanglement
- Has abstract in OpenAlex
- yes