Abstract
We study shape deformations of two-dimensional end-of-the-world (ETW) branes, such as those in bottom-up models of two-dimensional holographic boundary conformal field theories (BCFT), and derive an action for the theory of brane deformations in any bulk three-dimensional maximally symmetric spacetime. In the case of a bulk anti-de Sitter (AdS) spacetime, at leading order in the ultraviolet cutoff, the induced theory on the brane controlling its shape is Liouville gravity coupled to quantum matter. We show in certain limits the theory reduces to semi-classical AdS, dS or flat Jackiw-Teitelboim (JT) gravity, thus providing the first doubly-holographic derivation of two-dimensional models of dilaton gravity minimally coupled to a large number of conformal fields. Specializing to the AdS JT gravity limit, we discuss the dual BCFT interpretation and provide evidence that changing the boundary conditions of JT gravity on the brane is equivalent to a deformation of the dual BCFT with the displacement operator. This establishes a doubly-holographic triality between (i) brane deformations in the bulk, (ii) JT gravity in the brane description, and (iii) irrelevant deformations of the CFT boundary. Lastly, in the presence of a non-trivial dilaton profile, we prove that the Ryu-Takayanagi formula for holographic BCFTs receives a contact term whenever the minimal surface ends on the brane.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) R1005 [hep-th/9111056] [INSPIRE].
J.G. Russo, L. Susskind and L. Thorlacius, The Endpoint of Hawking radiation, Phys. Rev. D 46 (1992) 3444 [hep-th/9206070] [INSPIRE].
S.M. Christensen and S.A. Fulling, Trace Anomalies and the Hawking Effect, Phys. Rev. D 15 (1977) 2088 [INSPIRE].
A.M. Polyakov, Quantum Geometry of Bosonic Strings, Phys. Lett. B 103 (1981) 207 [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
T.M. Fiola, J. Preskill, A. Strominger and S.P. Trivedi, Black hole thermodynamics and information loss in two-dimensions, Phys. Rev. D 50 (1994) 3987 [hep-th/9403137] [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].
F.F. Gautason, L. Schneiderbauer, W. Sybesma and L. Thorlacius, Page Curve for an Evaporating Black Hole, JHEP 05 (2020) 091 [arXiv:2004.00598] [INSPIRE].
J.F. Pedraza, A. Svesko, W. Sybesma and M.R. Visser, Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity, JHEP 12 (2021) 134 [arXiv:2107.10358] [INSPIRE].
J.F. Pedraza, A. Svesko, W. Sybesma and M.R. Visser, Microcanonical action and the entropy of Hawking radiation, Phys. Rev. D 105 (2022) 126010 [arXiv:2111.06912] [INSPIRE].
A. Svesko, E. Verheijden, E.P. Verlinde and M.R. Visser, Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity, JHEP 08 (2022) 075 [arXiv:2203.00700] [INSPIRE].
S. Hirano, Island formula from Wald-like entropy with backreaction, JHEP 02 (2024) 125 [arXiv:2310.03416] [INSPIRE].
T. Hartman, E. Shaghoulian and A. Strominger, Islands in Asymptotically Flat 2D Gravity, JHEP 07 (2020) 022 [arXiv:2004.13857] [INSPIRE].
A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev/.
A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015, http://online.kitp.ucsb.edu/online/entangled15/kitaev2/.
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].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
A. Achucarro and M.E. Ortiz, Relating black holes in two-dimensions and three-dimensions, Phys. Rev. D 48 (1993) 3600 [hep-th/9304068] [INSPIRE].
A. Fabbri, D.J. Navarro and J. Navarro-Salas, Quantum evolution of near extremal Reissner-Nordstrom black holes, Nucl. Phys. B 595 (2001) 381 [hep-th/0006035] [INSPIRE].
P. Nayak et al., On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
S. Sachdev, Universal low temperature theory of charged black holes with AdS2 horizons, J. Math. Phys. 60 (2019) 052303 [arXiv:1902.04078] [INSPIRE].
A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS2/nCFT1 correspondence, JHEP 10 (2018) 042 [arXiv:1807.06988] [INSPIRE].
U. Moitra, S.K. Sake, S.P. Trivedi and V. Vishal, Jackiw-Teitelboim Gravity and Rotating Black Holes, JHEP 11 (2019) 047 [arXiv:1905.10378] [INSPIRE].
A. Castro, J.F. Pedraza, C. Toldo and E. Verheijden, Rotating 5D Black Holes: Interactions and deformations near extremality, SciPost Phys. 11 (2021) 102 [arXiv:2106.00649] [INSPIRE].
J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional Nearly de Sitter gravity, JHEP 01 (2021) 139 [arXiv:1904.01911] [INSPIRE].
J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, JHEP 06 (2020) 048 [arXiv:1905.03780] [INSPIRE].
W. Sybesma, Pure de Sitter space and the island moving back in time, Class. Quant. Grav. 38 (2021) 145012 [arXiv:2008.07994] [INSPIRE].
J. Kames-King, E.M.H. Verheijden and E.P. Verlinde, No Page curves for the de Sitter horizon, JHEP 03 (2022) 040 [arXiv:2108.09318] [INSPIRE].
A. Castro, F. Mariani and C. Toldo, Near-extremal limits of de Sitter black holes, JHEP 07 (2023) 131 [arXiv:2212.14356] [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].
S. de Haro, K. Skenderis and S.N. Solodukhin, Gravity in warped compactifications and the holographic stress tensor, Class. Quant. Grav. 18 (2001) 3171 [hep-th/0011230] [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
H.Z. Chen et al., Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane, JHEP 12 (2020) 025 [arXiv:2010.00018] [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].
H.Z. Chen et al., Quantum Extremal Islands Made Easy, Part I: Entanglement on the Brane, JHEP 10 (2020) 166 [arXiv:2006.04851] [INSPIRE].
G. Grimaldi, J. Hernandez and R.C. Myers, Quantum extremal islands made easy. Part IV. Massive black holes on the brane, JHEP 03 (2022) 136 [arXiv:2202.00679] [INSPIRE].
J.H. Lee, D. Neuenfeld and A. Shukla, Bounds on gravitational brane couplings and tomography in AdS3 black hole microstates, JHEP 10 (2022) 139 [arXiv:2206.06511] [INSPIRE].
T. Kawamoto, S.-M. Ruan and T. Takayanagia, Gluing AdS/CFT, JHEP 07 (2023) 080 [arXiv:2303.01247] [INSPIRE].
S. Carlip, Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity, Class. Quant. Grav. 22 (2005) 3055 [gr-qc/0501033] [INSPIRE].
K. Nguyen, Holographic boundary actions in AdS3/CFT2 revisited, JHEP 10 (2021) 218 [arXiv:2108.01095] [INSPIRE].
J. Garriga and T. Tanaka, Gravity in the brane world, Phys. Rev. Lett. 84 (2000) 2778 [hep-th/9911055] [INSPIRE].
U. Gen and M. Sasaki, Radion on the de Sitter brane, Prog. Theor. Phys. 105 (2001) 591 [gr-qc/0011078] [INSPIRE].
H. Kudoh and T. Tanaka, Second order perturbations in the Randall-Sundrum infinite brane world model, Phys. Rev. D 64 (2001) 084022 [hep-th/0104049] [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].
H. Geng et al., Information Transfer with a Gravitating Bath, SciPost Phys. 10 (2021) 103 [arXiv:2012.04671] [INSPIRE].
H. Geng et al., Inconsistency of islands in theories with long-range gravity, JHEP 01 (2022) 182 [arXiv:2107.03390] [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].
A. Bhattacharjee and M. Saha, JT gravity from holographic reduction of 3D asymptotically flat spacetime, JHEP 01 (2023) 138 [arXiv:2211.13415] [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].
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].
J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [INSPIRE].
G. Sárosi, AdS2 holography and the SYK model, PoS Modave2017 (2018) 001 [arXiv:1711.08482] [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].
J.W. York Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [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].
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].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
P. Kraus, F. Larsen and R. Siebelink, The gravitational action in asymptotically AdS and flat space-times, Nucl. Phys. B 563 (1999) 259 [hep-th/9906127] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS / CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
I. Papadimitriou and K. Skenderis, AdS / CFT correspondence and geometry, IRMA Lect. Math. Theor. Phys. 8 (2005) 73 [hep-th/0404176] [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].
P. Calabrese and J.L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152] [INSPIRE].
M. Fujita, T. Takayanagi and E. Tonni, Aspects of AdS/BCFT, JHEP 11 (2011) 043 [arXiv:1108.5152] [INSPIRE].
K. Suzuki and T. Takayanagi, BCFT and Islands in two dimensions, JHEP 06 (2022) 095 [arXiv:2202.08462] [INSPIRE].
R.C. Myers, S.-M. Ruan and T. Ugajin, Double holography of entangled universes, JHEP 07 (2024) 035 [arXiv:2403.17483] [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].
H. Erbin, Notes on 2d quantum gravity and Liouville theory, (2015).
C.P. Herzog, K.-W. Huang and K. Jensen, Universal Entanglement and Boundary Geometry in Conformal Field Theory, JHEP 01 (2016) 162 [arXiv:1510.00021] [INSPIRE].
L. Ciambelli, A. Delfante, R. Ruzziconi and C. Zwikel, Symmetries and charges in Weyl-Fefferman-Graham gauge, Phys. Rev. D 108 (2023) 126003 [arXiv:2308.15480] [INSPIRE].
L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50 (1994) 2700 [hep-th/9401070] [INSPIRE].
C.V. Johnson, Nonperturbative Jackiw-Teitelboim gravity, Phys. Rev. D 101 (2020) 106023 [arXiv:1912.03637] [INSPIRE].
A. Kar, L. Lamprou, C. Marteau and F. Rosso, A Matrix Model for Flat Space Quantum Gravity, JHEP 03 (2023) 249 [arXiv:2208.05974] [INSPIRE].
F. Rosso, A solvable model of flat space holography, JHEP 02 (2023) 037 [arXiv:2209.14372] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS2 holography and \( T\overline{T} \) , JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
J.M. Maldacena and A. Strominger, Semiclassical decay of near extremal five-branes, JHEP 12 (1997) 008 [hep-th/9710014] [INSPIRE].
G. Mandal, A.M. Sengupta and S.R. Wadia, Classical solutions of two-dimensional string theory, Mod. Phys. Lett. A 6 (1991) 1685 [INSPIRE].
E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].
S. Bose, L. Parker and Y. Peleg, Semiinfinite throat as the end state geometry of two-dimensional black hole evaporation, Phys. Rev. D 52 (1995) 3512 [hep-th/9502098] [INSPIRE].
L. Thorlacius, Black hole evolution, Nucl. Phys. B Proc. Suppl. 41 (1995) 245 [hep-th/9411020] [INSPIRE].
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cim. 4 (1972) 737 [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].
R.C. Myers, Black hole entropy in two-dimensions, Phys. Rev. D 50 (1994) 6412 [hep-th/9405162] [INSPIRE].
T. Jacobson, Black hole entropy and induced gravity, gr-qc/9404039 [INSPIRE].
V.P. Frolov, D.V. Fursaev and A.I. Zelnikov, Statistical origin of black hole entropy in induced gravity, Nucl. Phys. B 486 (1997) 339 [hep-th/9607104] [INSPIRE].
V.P. Frolov and D.V. Fursaev, Mechanism of generation of black hole entropy in Sakharov’s induced gravity, Phys. Rev. D 56 (1997) 2212 [hep-th/9703178] [INSPIRE].
R. Emparan, Black hole entropy as entanglement entropy: A Holographic derivation, JHEP 06 (2006) 012 [hep-th/0603081] [INSPIRE].
D. Neuenfeld and M. Srivastava, On the causality paradox and the Karch-Randall braneworld as an EFT, JHEP 10 (2023) 164 [arXiv:2307.10392] [INSPIRE].
S. Hawking, J.M. Maldacena and A. Strominger, de Sitter entropy, quantum entanglement and AdS / CFT, JHEP 05 (2001) 001 [hep-th/0002145] [INSPIRE].
D.V. Fursaev, Black hole thermodynamics, induced gravity and gravity in brane worlds, in the proceedings of the International Conference on Quantization, Gauge Theory, and Strings: Conference Dedicated to the Memory of Professor Efim Fradkin, Moscow, Russian Federation, June 05–10 (2000) [hep-th/0009164] [INSPIRE].
D.M. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary, Nucl. Phys. B 406 (1993) 655 [hep-th/9302068] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
P. Bueno, R. Emparan and Q. Llorens, Higher-curvature gravities from braneworlds and the holographic c-theorem, Phys. Rev. D 106 (2022) 044012 [arXiv:2204.13421] [INSPIRE].
R. Emparan, A.M. Frassino and B. Way, Quantum BTZ black hole, JHEP 11 (2020) 137 [arXiv:2007.15999] [INSPIRE].
R. Emparan et al., Black holes in dS3, JHEP 11 (2022) 073 [arXiv:2207.03302] [INSPIRE].
E. Panella and A. Svesko, Quantum Kerr-de Sitter black holes in three dimensions, JHEP 06 (2023) 127 [arXiv:2303.08845] [INSPIRE].
M. Banados, C. Teitelboim and J. Zanelli, The black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Banados, 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].
H. Geng, L. Randall and E. Swanson, BCFT in a black hole background: an analytical holographic model, JHEP 12 (2022) 056 [arXiv:2209.02074] [INSPIRE].
K. Jensen and A. Karch, Holographic Dual of an Einstein-Podolsky-Rosen Pair has a Wormhole, Phys. Rev. Lett. 111 (2013) 211602 [arXiv:1307.1132] [INSPIRE].
J. Sonner, Holographic Schwinger Effect and the Geometry of Entanglement, Phys. Rev. Lett. 111 (2013) 211603 [arXiv:1307.6850] [INSPIRE].
J.P.S. Lemos and P.M. Sa, The black holes of a general two-dimensional dilaton gravity theory, Phys. Rev. D 49 (1994) 2897 [gr-qc/9311008] [INSPIRE].
W. Sybesma, A zoo of deformed Jackiw-Teitelboim models near large dimensional black holes, JHEP 01 (2023) 141 [arXiv:2211.07927] [INSPIRE].
H. Kanda et al., AdS/BCFT with brane-localized scalar field, JHEP 03 (2023) 105 [arXiv:2302.03895] [INSPIRE].
H. Kanda et al., Entanglement phase transition in holographic pseudo entropy, JHEP 03 (2024) 060 [arXiv:2311.13201] [INSPIRE].
F. David, Conformal Field Theories Coupled to 2D Gravity in the Conformal Gauge, Mod. Phys. Lett. A 3 (1988) 1651 [INSPIRE].
J. Distler and H. Kawai, Conformal Field Theory and 2D Quantum Gravity, Nucl. Phys. B 321 (1989) 509 [INSPIRE].
V. Fateev, A.B. Zamolodchikov and A.B. Zamolodchikov, Boundary Liouville field theory. 1. Boundary state and boundary two point function, hep-th/0001012 [INSPIRE].
J. Teschner, Remarks on Liouville theory with boundary, PoS tmr2000 (2000) 041 [hep-th/0009138] [INSPIRE].
A.B. Zamolodchikov and A.B. Zamolodchikov, Liouville field theory on a pseudosphere, hep-th/0101152 [INSPIRE].
F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
L. McGough, M. Mezei and H. Verlinde, Moving the CFT into the bulk with \( T\overline{T} \), JHEP 04 (2018) 010 [arXiv:1611.03470] [INSPIRE].
E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press (2009) [https://doi.org/10.1017/CBO9780511606601] [INSPIRE].
Acknowledgments
We are grateful to Nele Callebaut, Roberto Emparan, Antonia Micol Frassino, Ben Freivogel, Hao Geng, Jani Kastikainen, Thomas Mertens, Rodolfo Panerai, Juan Pedraza, Shan-Ming Ruan, and Matteo Selle for useful correspondence. We also thank Antonia Micol Frassino for initial collaboration. DN acknowledges support from the Heising-Simons Foundation “Observational Signatures of Quantum Gravity” collaboration grant 2021-2817. AS is supported by STFC consolidated grant ST/X000753/1. WS is supported by the Simons Foundation through an “INI-Simons Postdoctoral Fellowship in Mathematics”. WS acknowledges support from the Icelandic Research Fund via the Grant of Excellence titled “Quantum Fields and Quantum Geometry”, and the University of Iceland Research Fund. WS thanks Juan Pedraza for his hospitality.
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: 2404.07260
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
Neuenfeld, D., Svesko, A. & Sybesma, W. Liouville gravity at the end of the world:deformed defects in AdS/BCFT. J. High Energ. Phys. 2024, 215 (2024). https://doi.org/10.1007/JHEP07(2024)215
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2024)215