Abstract
In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.
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Acknowledgments
We thank Don Marolf, Pratik Rath, and Zi-Yue Wang for interesting discussions, and especially Jiuci Xu for collaboration on related topics. 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 Numbers DE-SC0023275 and DE-SC0011702. X.D. and W.W.W. were supported in part by funds from the University of California. G.N.R. is supported by the James Arthur Postdoctoral Fellowship at New York University, and was supported at the Kavli Institute for Theoretical Physics by the Simons Foundation (Grant No. 216179) and the National Science Foundation (Grant No. NSF PHY-1748958) and at the University of California, Santa Barbara by the Fundamental Physics Fellowship. D.W. is supported by NSF grant PHY2107939. C-H.W. was supported in part by the Ministry of Education, Taiwan.
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Dong, X., Remmen, G.N., Wang, D. et al. Holographic entanglement from the UV to the IR. J. High Energ. Phys. 2023, 207 (2023). https://doi.org/10.1007/JHEP11(2023)207
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DOI: https://doi.org/10.1007/JHEP11(2023)207