Holographic Tensor Networks with Bulk Gauge Symmetries

Abstract

Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called "fixed-area states" with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial, n-dependent contributions to the Rényi entropy and Rényi mutual information from this area operator, a feature shared by general holographic states.

36 pages, 4 figures

References in corpus (6)

• Gravity and the Crossed Product
• Large N algebras and generalized entropy
• Generalized entropy for general subregions in quantum gravity
• Holographic entanglement negativity and replica symmetry breaking
• A Type $I$ Approximation of the Crossed Product
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Cited by in corpus (6)

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• Holographic Tensor Networks as Tessellations of Geometry
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity