Abstract
We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different.
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S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
G.R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D Minkowski space, Phys. Lett. B 485 (2000) 208 [hep-th/0005016] [INSPIRE].
A. Karch and L. Randall, Locally localized gravity, JHEP 05 (2001) 008 [hep-th/0011156] [INSPIRE].
A. Karch and L. Randall, Open and closed string interpretation of SUSY CFT’s on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [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].
C. Bachas, J. de Boer, R. Dijkgraaf and H. Ooguri, Permeable conformal walls and holography, JHEP 06 (2002) 027 [hep-th/0111210] [INSPIRE].
B. Freivogel, V.E. Hubeny, A. Maloney, R.C. Myers, M. Rangamani and S. Shenker, Inflation in AdS/CFT, JHEP 03 (2006) 007 [hep-th/0510046] [INSPIRE].
B. Freivogel, G.T. Horowitz and S. Shenker, Colliding with a crunching bubble, JHEP 05 (2007) 090 [hep-th/0703146] [INSPIRE].
J.L.F. Barbón and E. Rabinovici, Holography of AdS vacuum bubbles, JHEP 04 (2010) 123 [arXiv:1003.4966] [INSPIRE].
S. Banerjee, U. Danielsson, G. Dibitetto, S. Giri and M. Schillo, Emergent de Sitter Cosmology from Decaying Anti-de Sitter Space, Phys. Rev. Lett. 121 (2018) 261301 [arXiv:1807.01570] [INSPIRE].
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, 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].
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.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].
D. Bak, C. Kim, S.-H. Yi and J. Yoon, Unitarity of entanglement and islands in two-sided Janus black holes, JHEP 01 (2021) 155 [arXiv:2006.11717] [INSPIRE].
R. Emparan, A.M. Frassino and B. Way, Quantum BTZ black hole, JHEP 11 (2020) 137 [arXiv:2007.15999] [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].
I. Akal, Y. Kusuki, N. Shiba, T. Takayanagi and Z. Wei, Entanglement Entropy in a Holographic Moving Mirror and the Page Curve, Phys. Rev. Lett. 126 (2021) 061604 [arXiv:2011.12005] [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].
H. Geng et al., Information Transfer with a Gravitating Bath, arXiv:2012.04671 [INSPIRE].
J.D. Brown and C. Teitelboim, Neutralization of the Cosmological Constant by Membrane Creation, Nucl. Phys. B 297 (1988) 787 [INSPIRE].
H. Ooguri and T. Takayanagi, Cobordism Conjecture in AdS, arXiv:2006.13953 [INSPIRE].
S. Lanza, F. Marchesano, L. Martucci and I. Valenzuela, Swampland Conjectures for Strings and Membranes, JHEP 02 (2021) 006 [arXiv:2006.15154] [INSPIRE].
A. Bedroya, M. Montero, C. Vafa and I. Valenzuela, de Sitter Bubbles and the Swampland, arXiv:2008.07555 [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-de Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
P. Simidzija and M. Van Raamsdonk, Holo-ween, JHEP 12 (2020) 028 [arXiv:2006.13943] [INSPIRE].
Z. Fu and D. Marolf, Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT, JHEP 11 (2019) 040 [arXiv:1909.02505] [INSPIRE].
A. May and M.V. Raamsdonk, Interpolating between multi-boundary wormholes and single-boundary geometries in holography, arXiv:2011.14258 [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
T. Azeyanagi, A. Karch, T. Takayanagi and E.G. Thompson, Holographic calculation of boundary entropy, JHEP 03 (2008) 054 [arXiv:0712.1850] [INSPIRE].
C. Bachas, S. Chapman, D. Ge and G. Policastro, Energy Reflection and Transmission at 2D Holographic Interfaces, Phys. Rev. Lett. 125 (2020) 231602 [arXiv:2006.11333] [INSPIRE].
D. Bak, M. Gutperle and S. Hirano, A Dilatonic deformation of AdS5 and its field theory dual, JHEP 05 (2003) 072 [hep-th/0304129] [INSPIRE].
J. Gomis and C. Romelsberger, Bubbling Defect CFT’s, JHEP 08 (2006) 050 [hep-th/0604155] [INSPIRE].
O. Lunin, 1/2-BPS states in M-theory and defects in the dual CFTs, JHEP 10 (2007) 014 [arXiv:0704.3442] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. I. Local solution and supersymmetric Janus, JHEP 06 (2007) 021 [arXiv:0705.0022] [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS Type IIB interface solutions. II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].
E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Exact Half-BPS Flux Solutions in M-theory. I: Local Solutions, JHEP 08 (2008) 028 [arXiv:0806.0605] [INSPIRE].
E. D’Hoker, J. Estes, M. Gutperle and D. Krym, Janus solutions in M-theory, JHEP 06 (2009) 018 [arXiv:0904.3313] [INSPIRE].
M. Chiodaroli, M. Gutperle, L.-Y. Hung and D. Krym, String Junctions and Holographic Interfaces, Phys. Rev. D 83 (2011) 026003 [arXiv:1010.2758] [INSPIRE].
M. Chiodaroli, E. D’Hoker, Y. Guo and M. Gutperle, Exact half-BPS string-junction solutions in six-dimensional supergravity, JHEP 12 (2011) 086 [arXiv:1107.1722] [INSPIRE].
C. Bachas and J. Estes, Spin-2 spectrum of defect theories, JHEP 06 (2011) 005 [arXiv:1103.2800] [INSPIRE].
O. Aharony, L. Berdichevsky, M. Berkooz and I. Shamir, Near-horizon solutions for D3-branes ending on 5-branes, Phys. Rev. D 84 (2011) 126003 [arXiv:1106.1870] [INSPIRE].
B. Assel, C. Bachas, J. Estes and J. Gomis, Holographic Duals of D = 3 N = 4 Superconformal Field Theories, JHEP 08 (2011) 087 [arXiv:1106.4253] [INSPIRE].
D. Bak, M. Gutperle and R.A. Janik, Janus Black Holes, JHEP 10 (2011) 056 [arXiv:1109.2736] [INSPIRE].
N. Bobev, K. Pilch and N.P. Warner, Supersymmetric Janus Solutions in Four Dimensions, JHEP 06 (2014) 058 [arXiv:1311.4883] [INSPIRE].
C. Bachas, E. D’Hoker, J. Estes and D. Krym, M-theory Solutions Invariant under D(2, 1; γ) ⊕ D(2, 1; γ), Fortsch. Phys. 62 (2014) 207 [arXiv:1312.5477] [INSPIRE].
E. D’Hoker, M. Gutperle and C.F. Uhlemann, Warped AdS6 × S2 in Type IIB supergravity II: Global solutions and five-brane webs, JHEP 05 (2017) 131 [arXiv:1703.08186] [INSPIRE].
Y. Lozano, N.T. Macpherson, C. Núñez and A. Ramirez, AdS3 solutions in massive IIA, defect CFTs and T-duality, JHEP 12 (2019) 013 [arXiv:1909.11669] [INSPIRE].
Y. Lozano, C. Núñez, A. Ramirez and S. Speziali, M -strings and AdS3 solutions to M-theory with small \( \mathcal{N} \) = (0, 4) supersymmetry, JHEP 08 (2020) 118 [arXiv:2005.06561] [INSPIRE].
I. Arav, K.C.M. Cheung, J.P. Gauntlett, M.M. Roberts and C. Rosen, Superconformal RG interfaces in holography, JHEP 11 (2020) 168 [arXiv:2007.07891] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
A.R. Brown and A. Dahlen, On ‘nothing’ as an infinitely negatively curved spacetime, Phys. Rev. D 85 (2012) 104026 [arXiv:1111.0301] [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].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, The Gravity Dual of a Density Matrix, Class. Quant. Grav. 29 (2012) 155009 [arXiv:1204.1330] [INSPIRE].
A.C. Wall, Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy, Class. Quant. Grav. 31 (2014) 225007 [arXiv:1211.3494] [INSPIRE].
M. Headrick, V.E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy, JHEP 12 (2014) 162 [arXiv:1408.6300] [INSPIRE].
M. Van Raamsdonk, Lectures on Gravity and Entanglement, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, (2016) [DOI] [arXiv:1609.00026] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lect. Notes Phys. 931 (2017) 1 [arXiv:1609.01287] [INSPIRE].
C. Bachas and I. Brunner, Fusion of conformal interfaces, JHEP 02 (2008) 085 [arXiv:0712.0076] [INSPIRE].
E. Witten, Deformations of JT Gravity and Phase Transitions, arXiv:2006.03494 [INSPIRE].
M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc. 484 (1999) 147 [hep-th/9901148] [INSPIRE].
K. Skenderis and S.N. Solodukhin, Quantum effective action from the AdS /CFT correspondence, Phys. Lett. B 472 (2000) 316 [hep-th/9910023] [INSPIRE].
M. Rooman and P. Spindel, Uniqueness of the asymptotic AdS3 geometry, Class. Quant. Grav. 18 (2001) 2117 [gr-qc/0011005] [INSPIRE].
K. Krasnov, On holomorphic factorization in asymptotically AdS 3-D gravity, Class. Quant. Grav. 20 (2003) 4015 [hep-th/0109198] [INSPIRE].
G. Compère, P. Mao, A. Seraj and M.M. Sheikh-Jabbari, Symplectic and Killing symmetries of AdS3 gravity: holographic vs boundary gravitons, JHEP 01 (2016) 080 [arXiv:1511.06079] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
J.M. Maldacena and A. Strominger, AdS3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].
R. Dijkgraaf, J.M. Maldacena, G.W. Moore and E.P. Verlinde, A Black hole Farey tail, hep-th/0005003 [INSPIRE].
W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10 (1966) 1 [Erratum ibid. 48 (1967) 463] [INSPIRE].
K. Lanczos, Flächenhafte Verteilung der Materie in der Einsteinschen Gravitationstheorie, Annalen Phys. 379 (1924) 518.
C. Bachas, Asymptotic symmetries of AdS2 branes, in Meeting on Strings and Gravity: Tying the Forces Together, 2001 [hep-th/0205115] [INSPIRE].
B. Czech, P.H. Nguyen and S. Swaminathan, A defect in holographic interpretations of tensor networks, JHEP 03 (2017) 090 [arXiv:1612.05698] [INSPIRE].
M. Cvetič, S. Griffies and S.-J. Rey, Static domain walls in N = 1 supergravity, Nucl. Phys. B 381 (1992) 301 [hep-th/9201007] [INSPIRE].
M. Cvetič and H.H. Soleng, Supergravity domain walls, Phys. Rept. 282 (1997) 159 [hep-th/9604090] [INSPIRE].
A. Ceresole, G. Dall’Agata, A. Giryavets, R. Kallosh and A.D. Linde, Domain walls, near-BPS bubbles, and probabilities in the landscape, Phys. Rev. D 74 (2006) 086010 [hep-th/0605266] [INSPIRE].
A. Vilenkin and E.P.S. Shellard, Cosmic Strings and Other Topological Defects, Cambridge University Press, Cambridge (1994) [INSPIRE].
M. Chiodaroli, M. Gutperle and L.-Y. Hung, Boundary entropy of supersymmetric Janus solutions, JHEP 09 (2010) 082 [arXiv:1005.4433] [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].
J. Erdmenger, M. Flory, C. Hoyos, M.-N. Newrzella and J.M.S. Wu, Entanglement Entropy in a Holographic Kondo Model, Fortsch. Phys. 64 (2016) 109 [arXiv:1511.03666] [INSPIRE].
M. Gutperle and A. Trivella, Note on entanglement entropy and regularization in holographic interface theories, Phys. Rev. D 95 (2017) 066009 [arXiv:1611.07595] [INSPIRE].
O. Kenneth and I. Klich, Opposites attract: A Theorem about the Casimir force, Phys. Rev. Lett. 97 (2006) 160401 [quant-ph/0601011] [INSPIRE].
C.P. Bachas, Comment on the sign of the Casimir force, J. Phys. A 40 (2007) 9089 [quant-ph/0611082] [INSPIRE].
E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas, M. Van Raamsdonk and T. Wiseman, The Phase structure of low dimensional large N gauge theories on Tori, JHEP 01 (2006) 140 [hep-th/0508077] [INSPIRE].
C.A. Keller, Phase transitions in symmetric orbifold CFTs and universality, JHEP 03 (2011) 114 [arXiv:1101.4937] [INSPIRE].
A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes, JHEP 10 (2019) 062 [arXiv:1810.11442] [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Large AdS black holes from QFT, arXiv:1810.12067 [INSPIRE].
S. Choi, J. Kim, S. Kim and J. Nahmgoong, Comments on deconfinement in AdS/CFT, arXiv:1811.08646 [INSPIRE].
C. Copetti, A. Grassi, Z. Komargodski and L. Tizzano, Delayed Deconfinement and the Hawking-Page Transition, arXiv:2008.04950 [INSPIRE].
J.D. Marsano, Phase transitions in Yang-Mills theories and their gravity duals, UMI-32-17820 [INSPIRE].
S. Chapman, D. Ge and G. Policastro, Holographic Complexity for Defects Distinguishes Action from Volume, JHEP 05 (2019) 049 [arXiv:1811.12549] [INSPIRE].
C. Bachas, I. Brunner and D. Roggenkamp, A worldsheet extension of O(d, d : Z ), JHEP 10 (2012) 039 [arXiv:1205.4647] [INSPIRE].
C. Bachas, I. Brunner and D. Roggenkamp, Fusion of Critical Defect Lines in the 2D Ising Model, J. Stat. Mech. 1308 (2013) P08008 [arXiv:1303.3616] [INSPIRE].
D. Marolf, Black Holes, AdS, and CFTs, Gen. Rel. Grav. 41 (2009) 903 [arXiv:0810.4886] [INSPIRE].
C. Bachas and I. Lavdas, Quantum Gates to other Universes, Fortsch. Phys. 66 (2018) 1700096 [arXiv:1711.11372] [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, An Exact Construction of Codimension two Holography, JHEP 01 (2021) 150 [arXiv:2009.06263] [INSPIRE].
S. Zhao, C. Northe and R. Meyer, Symmetry-Resolved Entanglement in AdS3 /CFT2 coupled to U(1) Chern-Simons Theory, arXiv:2012.11274 [INSPIRE].
T. Takayanagi and K. Tamaoka, Gravity Edges Modes and Hayward Term, JHEP 02 (2020) 167 [arXiv:1912.01636] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
G. Hayward, Gravitational action for space-times with nonsmooth boundaries, Phys. Rev. D 47 (1993) 3275 [INSPIRE].
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Bachas, C., Papadopoulos, V. Phases of holographic interfaces. J. High Energ. Phys. 2021, 262 (2021). https://doi.org/10.1007/JHEP04(2021)262
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DOI: https://doi.org/10.1007/JHEP04(2021)262