Abstract
A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler wedges at a temperature T = 1/2π. We can gradually disentangle the state by lowering this temperature, and the entanglement entropy should vanish in the limit T → 0 to the Boulware vacuum. However, holography yields a non-zero entanglement entropy at arbitrarily low T, since the bridge in the bulk between the two wedges retains a finite width. We show how this is resolved by bulk quantum effects of the same kind that affect the entropy of near-extremal black holes. Specifically, a Weyl transformation maps the holographic Boulware states to near-extremal hyperbolic black holes. A reduction to an effective two-dimensional theory captures the large quantum fluctuations in the geometry of the bridge, which bring down to zero the density of entangled states in the Boulware vacuum. Using another Weyl transformation, we construct unentangled Boulware states in de Sitter space.
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Acknowledgments
We are grateful to José Barbón, Alex Belin, Alejandro Cabo-Bizet, Horacio Casini, Rob Myers, Martín Sasieta, Lenny Susskind, Tadashi Takayanagi, Marija Tomašević and Joaquín Turiaci for conversations. RE is supported by MICINN grants PID2019-105614GB-C22 and PID2022-136224NB-C22, AGAUR grant 2017-SGR 754, and State Research Agency of MICINN through the “Unit of Excellence María de Maeztu 2020-2023” award to the Institute of Cosmos Sciences (CEX2019-000918-M). JMM is supported by CONICET, Argentina. RE would like to thank the Isaac Newton Institute for Mathematical Sciences for support during the programme “Black holes: bridges between number theory and holographic quantum information” when work on this paper (on the destruction of bridges) was undertaken, supported by EPSRC Grant Number EP/R014604/1.
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Emparan, R., Magán, J.M. Tearing down spacetime with quantum disentanglement. J. High Energ. Phys. 2024, 78 (2024). https://doi.org/10.1007/JHEP03(2024)078
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DOI: https://doi.org/10.1007/JHEP03(2024)078