Abstract
Recently, certain holographic Weyl transformed CFT2 is proposed to capture the main features of the AdS3/BCFT2 correspondence [1, 2]. In this paper, by adapting the Weyl transformation, we simulate a generalized AdS/BCFT set-up where the fluctuation of the Karch-Randall (KR) brane is considered. In the gravity dual of the Weyl transformed CFT, the so-called cutoff brane induced by the Weyl transformation plays the same role as the KR brane. Unlike the non-fluctuating configuration, in the 2d effective theory the additional twist operator is inserted at a different place, compared with the one inserted on the brane. Though this is well-understood in the Weyl transformed CFT set-up, it is confusing in the AdS/BCFT set-up where the effective theory is supposed to locate on the brane. This confusion indicates that the KR brane may be emergent from the boundary CFT2 via the Weyl transformations.
We also calculate the balanced partial entanglement (BPE) in the fluctuating brane configurations and find it coincide with the entanglement wedge cross-section (EWCS). This is a non-trivial test for the correspondence between the BPE and the EWCS, and a non-trivial consistency check for the Weyl transformed CFT set-up.
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References
D. Basu, Q. Wen and S. Zhou, Entanglement Islands from Hilbert Space Reduction, arXiv:2211.17004 [INSPIRE].
D. Basu, J. Lin, Y. Lu and Q. Wen, Ownerless island and partial entanglement entropy in island phases, SciPost Phys. 15 (2023) 227 [arXiv:2305.04259] [INSPIRE].
J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
N. Engelhardt and A.C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime, JHEP 01 (2015) 073 [arXiv:1408.3203] [INSPIRE].
A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, JHEP 12 (2019) 063 [arXiv:1905.08762] [INSPIRE].
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [INSPIRE].
A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry, JHEP 03 (2020) 149 [arXiv:1908.10996] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Almheiri et al., Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
D. Marolf and H. Maxfield, Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information, JHEP 08 (2020) 044 [arXiv:2002.08950] [INSPIRE].
Y. Lu and J. Lin, The Markov gap in the presence of islands, JHEP 03 (2023) 043 [arXiv:2211.06886] [INSPIRE].
Y. Lu and J. Lin, Islands in Kaluza–Klein black holes, Eur. Phys. J. C 82 (2022) 132 [arXiv:2106.07845] [INSPIRE].
J. Kumar Basak et al., Islands for entanglement negativity, SciPost Phys. 12 (2022) 003 [arXiv:2012.03983] [INSPIRE].
M.-H. Yu, X.-H. Ge and C.-Y. Lu, Page curves for accelerating black holes, Eur. Phys. J. C 83 (2023) 1104 [arXiv:2306.11407] [INSPIRE].
R.-X. Miao, Entanglement island versus massless gravity, Eur. Phys. J. C 84 (2024) 123 [arXiv:2212.07645] [INSPIRE].
D. Li and R.-X. Miao, Massless entanglement islands in cone holography, JHEP 06 (2023) 056 [arXiv:2303.10958] [INSPIRE].
H. Geng and A. Karch, Massive islands, JHEP 09 (2020) 121 [arXiv:2006.02438] [INSPIRE].
F. Deng, J. Chu and Y. Zhou, Defect extremal surface as the holographic counterpart of Island formula, JHEP 03 (2021) 008 [arXiv:2012.07612] [INSPIRE].
Y. An and P. Cheng, Replica wormhole as a vacuum-to-vacuum transition, Eur. Phys. J. C 83 (2023) 341 [arXiv:2304.09432] [INSPIRE].
W.-C. Gan, D.-H. Du and F.-W. Shu, Island and Page curve for one-sided asymptotically flat black hole, JHEP 07 (2022) 020 [arXiv:2203.06310] [INSPIRE].
T. Hartman, Y. Jiang and E. Shaghoulian, Islands in cosmology, JHEP 11 (2020) 111 [arXiv:2008.01022] [INSPIRE].
K. Hashimoto, N. Iizuka and Y. Matsuo, Islands in Schwarzschild black holes, JHEP 06 (2020) 085 [arXiv:2004.05863] [INSPIRE].
Y. Ling, Y. Liu and Z.-Y. Xian, Island in Charged Black Holes, JHEP 03 (2021) 251 [arXiv:2010.00037] [INSPIRE].
I. Akal et al., Entanglement Entropy in a Holographic Moving Mirror and the Page Curve, Phys. Rev. Lett. 126 (2021) 061604 [arXiv:2011.12005] [INSPIRE].
X. Wang, R. Li and J. Wang, Islands and Page curves of Reissner-Nordström black holes, JHEP 04 (2021) 103 [arXiv:2101.06867] [INSPIRE].
Y. Guo and R.-X. Miao, Page curves on codim-m and charged branes, Eur. Phys. J. C 83 (2023) 847 [INSPIRE].
J.-C. Chang, S. He, Y.-X. Liu and L. Zhao, Island formula in Planck brane, JHEP 11 (2023) 006 [arXiv:2308.03645] [INSPIRE].
M. Afrasiar, J.K. Basak, A. Chandra and G. Sengupta, Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds, JHEP 02 (2023) 203 [arXiv:2211.13246] [INSPIRE].
H. Geng et al., Constraining braneworlds with entanglement entropy, SciPost Phys. 15 (2023) 199 [arXiv:2306.15672] [INSPIRE].
F. Deng, Z. Wang and Y. Zhou, End of the World Brane meets \( T\overline{T} \), arXiv:2310.15031 [INSPIRE].
K. Suzuki and T. Takayanagi, BCFT and Islands in two dimensions, JHEP 06 (2022) 095 [arXiv:2202.08462] [INSPIRE].
L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
H. Geng et al., Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, Phys. Rev. Lett. 129 (2022) 231601 [arXiv:2206.04695] [INSPIRE].
H. Geng, Aspects of AdS2 quantum gravity and the Karch-Randall braneworld, JHEP 09 (2022) 024 [arXiv:2206.11277] [INSPIRE].
F. Deng, Y.-S. An and Y. Zhou, JT gravity from partial reduction and defect extremal surface, JHEP 02 (2023) 219 [arXiv:2206.09609] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
B.M. Terhal, M. Horodecki, D.W. Leung and D.P. DiVincenzo, The entanglement of purification, J. Math. Phys. 43 (2002) 4286 [quant-ph/0202044] [INSPIRE].
T. Takayanagi and K. Umemoto, Entanglement of purification through holographic duality, Nature Phys. 14 (2018) 573 [arXiv:1708.09393] [INSPIRE].
P. Nguyen et al., Entanglement of purification: from spin chains to holography, JHEP 01 (2018) 098 [arXiv:1709.07424] [INSPIRE].
J. Kudler-Flam and S. Ryu, Entanglement negativity and minimal entanglement wedge cross sections in holographic theories, Phys. Rev. D 99 (2019) 106014 [arXiv:1808.00446] [INSPIRE].
Y. Kusuki, J. Kudler-Flam and S. Ryu, Derivation of holographic negativity in AdS3/CFT2, Phys. Rev. Lett. 123 (2019) 131603 [arXiv:1907.07824] [INSPIRE].
P. Chaturvedi, V. Malvimat and G. Sengupta, Holographic Quantum Entanglement Negativity, JHEP 05 (2018) 172 [arXiv:1609.06609] [INSPIRE].
S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section, JHEP 03 (2021) 178 [arXiv:1905.00577] [INSPIRE].
K. Tamaoka, Entanglement Wedge Cross Section from the Dual Density Matrix, Phys. Rev. Lett. 122 (2019) 141601 [arXiv:1809.09109] [INSPIRE].
R. Espíndola, A. Guijosa and J.F. Pedraza, Entanglement Wedge Reconstruction and Entanglement of Purification, Eur. Phys. J. C 78 (2018) 646 [arXiv:1804.05855] [INSPIRE].
C.A. Agón, J. De Boer and J.F. Pedraza, Geometric Aspects of Holographic Bit Threads, JHEP 05 (2019) 075 [arXiv:1811.08879] [INSPIRE].
J. Levin, O. DeWolfe and G. Smith, Correlation measures and distillable entanglement in AdS/CFT, Phys. Rev. D 101 (2020) 046015 [arXiv:1909.04727] [INSPIRE].
Q. Wen, Balanced Partial Entanglement and the Entanglement Wedge Cross Section, JHEP 04 (2021) 301 [arXiv:2103.00415] [INSPIRE].
Q. Wen and H. Zhong, Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies, SciPost Phys. 13 (2022) 056 [arXiv:2205.10858] [INSPIRE].
H.A. Camargo, P. Nandy, Q. Wen and H. Zhong, Balanced partial entanglement and mixed state correlations, SciPost Phys. 12 (2022) 137 [arXiv:2201.13362] [INSPIRE].
D. Basu, Balanced Partial Entanglement in Flat Holography, arXiv:2203.05491 [INSPIRE].
A. Bagchi, Correspondence between Asymptotically Flat Spacetimes and Nonrelativistic Conformal Field Theories, Phys. Rev. Lett. 105 (2010) 171601 [arXiv:1006.3354] [INSPIRE].
H. Jiang, W. Song and Q. Wen, Entanglement Entropy in Flat Holography, JHEP 07 (2017) 142 [arXiv:1706.07552] [INSPIRE].
A. Bhattacharya, A. Bhattacharyya and A.K. Patra, Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld, JHEP 07 (2023) 060 [arXiv:2304.09909] [INSPIRE].
S.E. Aguilar-Gutierrez, A.K. Patra and J.F. Pedraza, Entangled universes in dS wedge holography, JHEP 10 (2023) 156 [arXiv:2308.05666] [INSPIRE].
G. Vidal and Y. Chen, Entanglement contour, J. Stat. Mech. 2014 (2014) P10011 [arXiv:1406.1471] [INSPIRE].
Q. Wen, Fine structure in holographic entanglement and entanglement contour, Phys. Rev. D 98 (2018) 106004 [arXiv:1803.05552] [INSPIRE].
J. Kudler-Flam, I. MacCormack and S. Ryu, Holographic entanglement contour, bit threads, and the entanglement tsunami, J. Phys. A 52 (2019) 325401 [arXiv:1902.04654] [INSPIRE].
M. Han and Q. Wen, Entanglement entropy from entanglement contour: higher dimensions, SciPost Phys. Core 5 (2022) 020 [arXiv:1905.05522] [INSPIRE].
Q. Wen, Formulas for Partial Entanglement Entropy, Phys. Rev. Res. 2 (2020) 023170 [arXiv:1910.10978] [INSPIRE].
Q. Wen, Entanglement contour and modular flow from subset entanglement entropies, JHEP 05 (2020) 018 [arXiv:1902.06905] [INSPIRE].
M. Han and Q. Wen, First law and quantum correction for holographic entanglement contour, SciPost Phys. 11 (2021) 058 [arXiv:2106.12397] [INSPIRE].
D.S. Ageev, Shaping contours of entanglement islands in BCFT, JHEP 03 (2022) 033 [arXiv:2107.09083] [INSPIRE].
A. Rolph, Local measures of entanglement in black holes and CFTs, SciPost Phys. 12 (2022) 079 [arXiv:2107.11385] [INSPIRE].
Y.-Y. Lin, J.-R. Sun, Y. Sun and J.-C. Jin, The PEE aspects of entanglement islands from bit threads, JHEP 07 (2022) 009 [arXiv:2203.03111] [INSPIRE].
Y.-Y. Lin, Distilled density matrices of holographic partial entanglement entropy from thread-state correspondence, Phys. Rev. D 108 (2023) 106010 [arXiv:2305.02895] [INSPIRE].
Y. Liu, Revisiting 3D Flat Holography: Causality Structure and Modular flow, arXiv:2309.05220 [INSPIRE].
J. Lin, Y. Lu and Q. Wen, Geometrizing the partial entanglement entropy: from PEE threads to bit threads, JHEP 02 (2024) 191 [arXiv:2311.02301] [INSPIRE].
H. Casini and M. Huerta, Remarks on the entanglement entropy for disconnected regions, JHEP 03 (2009) 048 [arXiv:0812.1773] [INSPIRE].
Y. Zou et al., Universal tripartite entanglement in one-dimensional many-body systems, Phys. Rev. Lett. 126 (2021) 120501 [arXiv:2011.11864] [INSPIRE].
P. Hayden, O. Parrikar and J. Sorce, The Markov gap for geometric reflected entropy, JHEP 10 (2021) 047 [arXiv:2107.00009] [INSPIRE].
T. Hartman, Entanglement Entropy at Large Central Charge, arXiv:1303.6955 [INSPIRE].
J. Lin, Y. Lu and Q. Wen, Partial entanglement network and bulk geometry reconstruction in AdS/CFT, arXiv:2401.07471 [INSPIRE].
Q. Wen, M. Xu and H. Zhong, A Reformulation of the Island Formula from the PEE threads, to appear.
P. Caputa et al., Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories, Phys. Rev. Lett. 119 (2017) 071602 [arXiv:1703.00456] [INSPIRE].
P. Caputa, M. Miyaji, T. Takayanagi and K. Umemoto, Holographic Entanglement of Purification from Conformal Field Theories, Phys. Rev. Lett. 122 (2019) 111601 [arXiv:1812.05268] [INSPIRE].
A. Chandra, Z. Li and Q. Wen, Entanglement islands and cutoff branes from path-integral optimization, arXiv:2402.15836 [INSPIRE].
J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP 2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
H. Geng et al., Information Transfer with a Gravitating Bath, SciPost Phys. 10 (2021) 103 [arXiv:2012.04671] [INSPIRE].
Q. Wen, Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals, JHEP 01 (2019) 220 [arXiv:1810.11756] [INSPIRE].
Acknowledgments
We would like to thank Hao Geng, Ziming Ji, Zhenbin Yang and Yang Zhou for helpful discussions. J. Lin is supported by the National Natural Science Foundation of China under Grant No. 12247117, No. 12247103 and No. 12047502. Y. Lu receives support from the China Postdoctoral Science Foundation under Grant No. 2022TQ0140, the National Natural Science Foundation of China under Grant No. 12247161, and the NSFC Research Fund for International Scientists (Grant No. 12250410250).
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ArXiv ePrint: 2312.03531
Jiong Lin and Yizhou Lu are co-first authors.
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Lin, J., Lu, Y. & Wen, Q. Cutoff brane vs the Karch-Randall brane: the fluctuating case. J. High Energ. Phys. 2024, 17 (2024). https://doi.org/10.1007/JHEP06(2024)017
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DOI: https://doi.org/10.1007/JHEP06(2024)017