We explore the entanglement evolution of boundary intervals in eternal Janus black holes that can be embedded consistently into string theory in the low-energy limit. By studying the geodesics we show that there is a transition in the entanglement characteristic around the Page time, which manifests the unitarity of the evolution. We reproduce and reinterpret these bulk results from two different lower-dimensional perspectives: first as an interface CFT in the usual AdS/CFT correspondence and second as an effective gravity theory in one lower dimension coupled to a radiation background. In the limit where the number of interface degrees of freedom becomes large, we obtain an effective theory on appropriate branes that replace the deep interior region in the bulk, coined the shadow region. In this effective theory, we also identify the island of the radiation entanglement wedge and verify the newly proposed quantum extremization method. Our model clarifies that double holography with gravity in two higher dimensions can be realized in a concrete and consistent way and that the occurrence of islands is natural in one higher dimension. Furthermore, our model reveals that there can be a transitional behavior of the Page curve before the Page time, which is related to the emergence of new matter degrees of freedom on the branes.
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].
R.M. Wald, On Particle Creation by Black Holes, Commun. Math. Phys. 45 (1975) 9 [INSPIRE].
J. Polchinski, The Black Hole Information Problem, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, Boulder U.S.A. (2015), pg. 353 [arXiv:1609.04036] [INSPIRE].
J. Maldacena, Black holes and quantum information, Nature Rev. Phys. 2 (2020) 123.
S.W. Hawking, The Unpredictability of Quantum Gravity, Commun. Math. Phys. 87 (1982) 395 [INSPIRE].
T. Banks, L. Susskind and M.E. Peskin, Difficulties for the Evolution of Pure States Into Mixed States, Nucl. Phys. B 244 (1984) 125.
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
P. Hayden et al., Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality, Commun. Math. Phys. 246 (2004) 359.
F.W. Olver, D.W. Lozier, R.F. Boisvert and C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, New York U.S.A. (2010).
I. Papadimitriou, Janus effective action, unpublished note.
I. Papadimitriou, Lectures on Holographic Renormalization, Springer Proc. Phys. 176 (2016) 131 [INSPIRE].
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ArXiv ePrint: 2006.11717
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Bak, D., Kim, C., Yi, SH. et al. Unitarity of entanglement and islands in two-sided Janus black holes. J. High Energ. Phys. 2021, 155 (2021). https://doi.org/10.1007/JHEP01(2021)155
- AdS-CFT Correspondence
- Black Holes
- 2D Gravity