Living on the edge: a toy model for holographic reconstruction of algebras with centers

A bstract We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network...

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Bibliographic Details
Published in:The journal of high energy physics 2017-04, Vol.2017 (4), p.1-18, Article 93
Main Authors: Donnelly, William, Marolf, Donald, Michel, Ben, Wien, Jason
Format: Article
Language:English
Subjects:
AdS-CFT Correspondence
Algebra
Boundaries
Classical and Quantum Gravitation
Electric fields
Elementary Particles
Entanglement
Entropy
Error correcting codes
Error correction
Error correction & detection
Gauge Symmetry
Gravitons
High energy physics
Hilbert space
Mathematical analysis
Models of Quantum Gravity
Physics
Physics and Astronomy
Quantum entanglement
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Reconstruction
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Tensors
Yang-Mills theory
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Summary:A bstract We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary bounda ry regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the δ Area 4 G N term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this δ Area 4 G N term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2017)093