Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers

Abstract

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 boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the $\frac{\delta \text{Area}}{4G_N}$ term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this $\frac{\delta \text{Area}}{4G_N}$ term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.

arXiv comment20 pages, 11 figures

References in corpus (17)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• Quantum corrections to holographic entanglement entropy
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Holographic duality from random tensor networks
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Local subsystems in gauge theory and gravity
• Remarks on entanglement entropy for gauge fields
• Decomposition of entanglement entropy in lattice gauge theory
• Entanglement entropy of electromagnetic edge modes
• Entanglement entropy in gauge theories and the holographic principle for electric strings
• On The Entanglement Entropy For Gauge Theories
• Entanglement entropy and nonabelian gauge symmetry
• Geometric entropy and edge modes of the electromagnetic field
• Exact holographic mapping and emergent space-time geometry
• Bidirectional holographic codes and sub-AdS locality

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