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.
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Acknowledgments
We thank Chris Akers, Horacio Casini, David Grabovsky, Daniel Harlow, Kristan Jensen, Don Marolf, and Pratik Rath for interesting discussions. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-19-1-0360. This material is also based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011702. SAM would like to thank the Centro de Ciencias de Benasque Pedro Pascal for their hospitality while a portion of this work was completed.
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Dong, X., McBride, S. & Weng, W.W. Holographic tensor networks with bulk gauge symmetries. J. High Energ. Phys. 2024, 222 (2024). https://doi.org/10.1007/JHEP02(2024)222
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DOI: https://doi.org/10.1007/JHEP02(2024)222