Abstract
The previous studies of the island and double holography mainly focus on codimension-one branes. This paper explores the island on the codimension-two brane in AdS/dCFT. The codimension-two brane is closely related to conical singularity, which is very different from the codimension-one brane. We analyze the mass spectrum of gravitons on the codimension-two brane and find that the larger the brane tension is, the smaller the gravitational mass is. The massless mode is forbidden by either the boundary or normalization conditions. We prove that the first massive gravitational mode is located on the codimension-two brane; the larger the tension, the better the localization. It is similar to the case of codimension-one brane and builds an excellent physical foundation for the study of black hole evolution on codimension-two branes. We find that the Page curve of eternal black holes can be recovered due to the island ending on the codimension-two brane. The new feature is that the extremal surface passing the horizon cannot be defined after some finite time in the no-island phase. Fortunately, this unusual situation does not affect the Page curve since it happens after Page time.
Article PDF
Similar content being viewed by others
References
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox, JHEP 09 (2020) 002 [arXiv:1905.08255] [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].
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93 (2021) 035002 [arXiv:2006.06872] [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].
M. Rozali, J. Sully, M. Van Raamsdonk, C. Waddell and D. Wakeham, Information radiation in BCFT models of black holes, JHEP 05 (2020) 004 [arXiv:1910.12836] [INSPIRE].
H.Z. Chen, Z. Fisher, J. Hernandez, R.C. Myers and S.-M. Ruan, Information Flow in Black Hole Evaporation, JHEP 03 (2020) 152 [arXiv:1911.03402] [INSPIRE].
A. Almheiri, R. Mahajan and J. Maldacena, Islands outside the horizon, arXiv:1910.11077 [INSPIRE].
A. Almheiri, R. Mahajan and J.E. Santos, Entanglement islands in higher dimensions, SciPost Phys. 9 (2020) 001 [arXiv:1911.09666] [INSPIRE].
Y. Kusuki, Y. Suzuki, T. Takayanagi and K. Umemoto, Looking at Shadows of Entanglement Wedges, PTEP 2020 (2020) 11B105 [arXiv:1912.08423] [INSPIRE].
V. Balasubramanian, A. Kar, O. Parrikar, G. Sárosi and T. Ugajin, Geometric secret sharing in a model of Hawking radiation, JHEP 01 (2021) 177 [arXiv:2003.05448] [INSPIRE].
H. Geng and A. Karch, Massive islands, JHEP 09 (2020) 121 [arXiv:2006.02438] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy. Part I. Entanglement on the Brane, JHEP 10 (2020) 166 [arXiv:2006.04851] [INSPIRE].
Y. Ling, Y. Liu and Z.-Y. Xian, Island in Charged Black Holes, JHEP 03 (2021) 251 [arXiv:2010.00037] [INSPIRE].
K. Kawabata, T. Nishioka, Y. Okuyama and K. Watanabe, Probing Hawking radiation through capacity of entanglement, JHEP 05 (2021) 062 [arXiv:2102.02425] [INSPIRE].
A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model, JHEP 05 (2021) 135 [arXiv:2103.15852] [INSPIRE].
K. Kawabata, T. Nishioka, Y. Okuyama and K. Watanabe, Replica wormholes and capacity of entanglement, JHEP 10 (2021) 227 [arXiv:2105.08396] [INSPIRE].
H. Geng et al., Inconsistency of islands in theories with long-range gravity, JHEP 01 (2022) 182 [arXiv:2107.03390] [INSPIRE].
C. Krishnan, Critical Islands, JHEP 01 (2021) 179 [arXiv:2007.06551] [INSPIRE].
H.Z. Chen, R.C. Myers, D. Neuenfeld, I.A. Reyes and J. Sandor, Quantum Extremal Islands Made Easy. Part II. Black Holes on the Brane, JHEP 12 (2020) 025 [arXiv:2010.00018] [INSPIRE].
K. Ghosh and C. Krishnan, Dirichlet baths and the not-so-fine-grained Page curve, JHEP 08 (2021) 119 [arXiv:2103.17253] [INSPIRE].
H. Omiya and Z. Wei, Causal structures and nonlocality in double holography, JHEP 07 (2022) 128 [arXiv:2107.01219] [INSPIRE].
A. Bhattacharya, A. Bhattacharyya, P. Nandy and A.K. Patra, Bath deformations, islands, and holographic complexity, Phys. Rev. D 105 (2022) 066019 [arXiv:2112.06967] [INSPIRE].
H. Geng et al., Entanglement phase structure of a holographic BCFT in a black hole background, JHEP 05 (2022) 153 [arXiv:2112.09132] [INSPIRE].
P.-C. Sun, Entanglement Islands from Holographic Thermalization of Rotating Charged Black Hole, arXiv:2108.12557 [INSPIRE].
C.-J. Chou, H.B. Lao and Y. Yang, Page curve of effective Hawking radiation, Phys. Rev. D 106 (2022) 066008 [arXiv:2111.14551] [INSPIRE].
B. Ahn, S.-E. Bak, H.-S. Jeong, K.-Y. Kim and Y.-W. Sun, Islands in charged linear dilaton black holes, Phys. Rev. D 105 (2022) 046012 [arXiv:2107.07444] [INSPIRE].
S. He, Y. Sun, L. Zhao and Y.-X. Zhang, The universality of islands outside the horizon, JHEP 05 (2022) 047 [arXiv:2110.07598] [INSPIRE].
M. Alishahiha, A. Faraji Astaneh and A. Naseh, Island in the presence of higher derivative terms, JHEP 02 (2021) 035 [arXiv:2005.08715] [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].
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].
F. Omidi, Entropy of Hawking radiation for two-sided hyperscaling violating black branes, JHEP 04 (2022) 022 [arXiv:2112.05890] [INSPIRE].
Q.-L. Hu, D. Li, R.-X. Miao and Y.-Q. Zeng, AdS/BCFT and Island for curvature-squared gravity, JHEP 09 (2022) 037 [arXiv:2202.03304] [INSPIRE].
S. Azarnia, R. Fareghbal, A. Naseh and H. Zolfi, Islands in flat-space cosmology, Phys. Rev. D 104 (2021) 126017 [arXiv:2109.04795] [INSPIRE].
T. Anous, M. Meineri, P. Pelliconi and J. Sonner, Sailing past the End of the World and discovering the Island, SciPost Phys. 13 (2022) 075 [arXiv:2202.11718] [INSPIRE].
A. Saha, S. Gangopadhyay and J.P. Saha, Mutual information, islands in black holes and the Page curve, Eur. Phys. J. C 82 (2022) 476 [arXiv:2109.02996] [INSPIRE].
G. Yadav and A. Misra, (”Swiss-Cheese”) Entanglement Entropy when Page-ing Theory Dual of Thermal QCD Above Tc at Intermediate Coupling, arXiv:2207.04048 [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].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].
M. Nozaki, T. Takayanagi and T. Ugajin, Central Charges for BCFTs and Holography, JHEP 06 (2012) 066 [arXiv:1205.1573] [INSPIRE].
R.-X. Miao, Holographic BCFT with Dirichlet Boundary Condition, JHEP 02 (2019) 025 [arXiv:1806.10777] [INSPIRE].
R.-X. Miao, C.-S. Chu and W.-Z. Guo, New proposal for a holographic boundary conformal field theory, Phys. Rev. D 96 (2017) 046005 [arXiv:1701.04275] [INSPIRE].
C.-S. Chu, R.-X. Miao and W.-Z. Guo, On New Proposal for Holographic BCFT, JHEP 04 (2017) 089 [arXiv:1701.07202] [INSPIRE].
C.-S. Chu and R.-X. Miao, Conformal boundary condition and massive gravitons in AdS/BCFT, JHEP 01 (2022) 084 [arXiv:2110.03159] [INSPIRE].
I. Akal, Y. Kusuki, T. Takayanagi and Z. Wei, Codimension two holography for wedges, Phys. Rev. D 102 (2020) 126007 [arXiv:2007.06800] [INSPIRE].
R.-X. Miao, Codimension-n holography for cones, Phys. Rev. D 104 (2021) 086031 [arXiv:2101.10031] [INSPIRE].
P.-J. Hu and R.-X. Miao, Effective action, spectrum and first law of wedge holography, JHEP 03 (2022) 145 [arXiv:2201.02014] [INSPIRE].
R.-X. Miao, An Exact Construction of Codimension two Holography, JHEP 01 (2021) 150 [arXiv:2009.06263] [INSPIRE].
H. Geng et al., Information Transfer with a Gravitating Bath, SciPost Phys. 10 (2021) 103 [arXiv:2012.04671] [INSPIRE].
H. Geng et al., Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld, arXiv:2206.04695 [INSPIRE].
H. Geng, Aspects of AdS2 quantum gravity and the Karch-Randall braneworld, JHEP 09 (2022) 024 [arXiv:2206.11277] [INSPIRE].
N. Ogawa, T. Takayanagi, T. Tsuda and T. Waki, Wedge Holography in Flat Space and Celestial Holography, arXiv:2207.06735 [INSPIRE].
K. Izumi, T. Shiromizu, K. Suzuki, T. Takayanagi and N. Tanahashi, Brane dynamics of holographic BCFTs, JHEP 10 (2022) 050 [arXiv:2205.15500] [INSPIRE].
K. Suzuki and T. Takayanagi, BCFT and Islands in two dimensions, JHEP 06 (2022) 095 [arXiv:2202.08462] [INSPIRE].
T. Numasawa and I. Tsiares, Universal dynamics of heavy operators in boundary CFT2, JHEP 08 (2022) 156 [arXiv:2202.01633] [INSPIRE].
Y. Kusuki, Analytic bootstrap in 2D boundary conformal field theory: towards braneworld holography, JHEP 03 (2022) 161 [arXiv:2112.10984] [INSPIRE].
Y. Aghababaie et al., Warped brane worlds in six-dimensional supergravity, JHEP 09 (2003) 037 [hep-th/0308064] [INSPIRE].
J.M. Cline, J. Descheneau, M. Giovannini and J. Vinet, Cosmology of codimension two brane worlds, JHEP 06 (2003) 048 [hep-th/0304147] [INSPIRE].
H. Hayashi, T. Kawano, Y. Tsuchiya and T. Watari, Flavor Structure in F-theory Compactifications, JHEP 08 (2010) 036 [arXiv:0910.2762] [INSPIRE].
O. Corradini, A. Iglesias, Z. Kakushadze and P. Langfelder, Gravity on a 3-brane in 6-D bulk, Phys. Lett. B 521 (2001) 96 [hep-th/0108055] [INSPIRE].
C. de Rham and A.J. Tolley, Gravitational waves in a codimension two braneworld, JCAP 02 (2006) 003 [hep-th/0511138] [INSPIRE].
K. Jensen and A. O’Bannon, Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects, Phys. Rev. D 88 (2013) 106006 [arXiv:1309.4523] [INSPIRE].
O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
X. Dong, The Gravity Dual of Renyi Entropy, Nature Commun. 7 (2016) 12472 [arXiv:1601.06788] [INSPIRE].
P. Bostock, R. Gregory, I. Navarro and J. Santiago, Einstein gravity on the codimension 2-brane?, Phys. Rev. Lett. 92 (2004) 221601 [hep-th/0311074] [INSPIRE].
S.Y. Li, No-Go Theorems on Localization of Gravity around Higher Codimensional Branes in Noncompact Extra Dimensions, JHEP 03 (2021) 063 [arXiv:2012.06409] [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
N. Kobayashi, T. Nishioka, Y. Sato and K. Watanabe, Towards a C-theorem in defect CFT, JHEP 01 (2019) 039 [arXiv:1810.06995] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
D. Carmi, S. Chapman, H. Marrochio, R.C. Myers and S. Sugishita, On the Time Dependence of Holographic Complexity, JHEP 11 (2017) 188 [arXiv:1709.10184] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2208.11982
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Hu, PJ., Li, D. & Miao, RX. Island on codimension-two branes in AdS/dCFT. J. High Energ. Phys. 2022, 8 (2022). https://doi.org/10.1007/JHEP11(2022)008
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2022)008