Abstract
We use holography to study the spectra of boundary conformal field theories (BCFTs). To do so, we consider a 2-dimensional Euclidean BCFT with two circular boundaries that correspond to dynamical end-of-the-world branes in 3-dimensional gravity. Interactions between these branes inform the operator content and the energy spectrum of the dual BCFT. As a proof of concept, we first consider two highly separated branes whose only interaction is taken to be mediated by a scalar field. The holographic computation of the scalar-mediated exchange reproduces a light scalar primary and its global descendants in the closed-string channel of the dual BCFT. We then consider a gravity model with point particles. Here, the interaction of two separated branes corresponds to a heavy operator which lies below the black hole threshold. However, we may also consider branes at finite separation that “merge” non-smoothly. Such brane mergers can be used to describe unitary sub-threshold boundary-condition-changing operators in the open-string spectrum of the BCFT. We also find a new class of sub-threshold Euclidean bra-ket wormhole saddles with a factorization puzzle for closed-string amplitudes.
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References
J.L. Cardy, Conformal invariance and surface critical behavior, Nucl. Phys. B 240 (1984) 514 [INSPIRE].
D.M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].
J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [INSPIRE].
I. Affleck, Conformal field theory approach to the Kondo effect, Acta Phys. Polon. B 26 (1995) 1869 [cond-mat/9512099] [INSPIRE].
I. Affleck, Conformal field theory approach to quantum impurity problems, in Field theories for low-dimensional condensed matter systems, Springer (2000), p. 117.
A. Sagnotti, Open strings and their symmetry groups, in NATO advanced summer institute on nonperturbative quantum field theory (Cargese summer institute), (1987) [hep-th/0208020] [INSPIRE].
J. Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724 [hep-th/9510017] [INSPIRE].
M.R. Gaberdiel, D-branes from conformal field theory, Fortsch. Phys. 50 (2002) 783 [hep-th/0201113] [INSPIRE].
A. Recknagel and V. Schomerus, Boundary conformal field theory and the worldsheet approach to D-branes, Cambridge University Press (2013) [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].
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].
A. Karch, J. Sully, C.F. Uhlemann and D.G.E. Walker, Boundary kinematic space, JHEP 08 (2017) 039 [arXiv:1703.02990] [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].
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. 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].
J. Sully, M.V. Raamsdonk and D. Wakeham, BCFT entanglement entropy at large central charge and the black hole interior, JHEP 03 (2021) 167 [arXiv:2004.13088] [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].
H. Geng, S. Lüst, R.K. Mishra and D. Wakeham, Holographic BCFTs and communicating black holes, jhep 08 (2021) 003 [arXiv:2104.07039] [INSPIRE].
D.S. Ageev, Shaping contours of entanglement islands in BCFT, JHEP 03 (2022) 033 [arXiv:2107.09083] [INSPIRE].
T.J. Hollowood, S.P. Kumar, A. Legramandi and N. Talwar, Ephemeral islands, plunging quantum extremal surfaces and BCFT channels, JHEP 01 (2022) 078 [arXiv:2109.01895] [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].
H. Geng, L. Randall and E. Swanson, BCFT in a black hole background: an analytical holographic model, arXiv:2209.02074 [INSPIRE].
E. D’Hoker, J. Estes and M. Gutperle, Exact half-BPS type IIB interface solutions. Part 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. Part II. Flux solutions and multi-Janus, JHEP 06 (2007) 022 [arXiv:0705.0024] [INSPIRE].
D. Gaiotto and E. Witten, Supersymmetric boundary conditions in N = 4 super Yang-Mills theory, J. Statist. Phys. 135 (2009) 789 [arXiv:0804.2902] [INSPIRE].
D. Gaiotto and E. Witten, S-duality of boundary conditions in N = 4 super Yang-Mills theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [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].
M. Chiodaroli, E. D’Hoker and M. Gutperle, Simple holographic duals to boundary CFTs, JHEP 02 (2012) 005 [arXiv:1111.6912] [INSPIRE].
M. Chiodaroli, E. D’Hoker and M. Gutperle, Holographic duals of boundary CFTs, JHEP 07 (2012) 177 [arXiv:1205.5303] [INSPIRE].
L. Berdichevsky and B.-E. Dahan, Local gravitational solutions dual to M2-branes intersecting and/or ending on M5-branes, JHEP 08 (2013) 061 [arXiv:1304.4389] [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].
C.F. Uhlemann, Islands and Page curves in 4d from type IIB, JHEP 08 (2021) 104 [arXiv:2105.00008] [INSPIRE].
C.F. Uhlemann, Information transfer with a twist, JHEP 01 (2022) 126 [arXiv:2111.11443] [INSPIRE].
L. Coccia and C.F. Uhlemann, Mapping out the internal space in AdS/BCFT with Wilson loops, JHEP 03 (2022) 127 [arXiv:2112.14648] [INSPIRE].
E.J. Martinec, A defect in AdS3/CFT2 duality, JHEP 06 (2022) 024 [arXiv:2201.04218] [INSPIRE].
A. Karch, H. Sun and C.F. Uhlemann, Double holography in string theory, JHEP 10 (2022) 012 [arXiv:2206.11292] [INSPIRE].
I. Affleck and A.W.W. Ludwig, The Fermi edge singularity and boundary condition changing operators, J. Phys. A 27 (1994) 5375 [cond-mat/9405057].
M. Miyaji, T. Takayanagi and T. Ugajin, Spectrum of end of the world branes in holographic BCFTs, JHEP 06 (2021) 023 [arXiv:2103.06893] [INSPIRE].
J. Kastikainen and S. Shashi, Structure of holographic BCFT correlators from geodesics, Phys. Rev. D 105 (2022) 046007 [arXiv:2109.00079] [INSPIRE].
Y. Chen, V. Gorbenko and J. Maldacena, Bra-ket wormholes in gravitationally prepared states, JHEP 02 (2021) 009 [arXiv:2007.16091] [INSPIRE].
N. Ishibashi, The boundary and crosscap states in conformal field theories, Mod. Phys. Lett. A 4 (1989) 251 [INSPIRE].
T. Onogi and N. Ishibashi, Conformal field theories on surfaces with boundaries and crosscaps, Mod. Phys. Lett. A 4 (1989) 161 [Erratum ibid. 4 (1989) 885] [INSPIRE].
J.L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl. Phys. B 324 (1989) 581 [INSPIRE].
G. Hayward, Gravitational action for space-times with nonsmooth boundaries, Phys. Rev. D 47 (1993) 3275 [INSPIRE].
M. Miyaji and C. Murdia, Holographic BCFT with a defect on the end-of-the-world brane, arXiv:2208.13783 [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
R.E. Behrend, P.A. Pearce, V.B. Petkova and J.-B. Zuber, Boundary conditions in rational conformal field theories, Nucl. Phys. B 570 (2000) 525 [hep-th/9908036] [INSPIRE].
J. Lacki, M. Ruiz-Altaba and P. Zaugg, Modular transformations of c ≥ 1 Virasoro characters, Phys. Lett. B 247 (1990) 493 [INSPIRE].
I. Affleck and A.W.W. Ludwig, Universal noninteger ‘ground state degeneracy’ in critical quantum systems, Phys. Rev. Lett. 67 (1991) 161 [INSPIRE].
D. Friedan and A. Konechny, On the boundary entropy of one-dimensional quantum systems at low temperature, Phys. Rev. Lett. 93 (2004) 030402 [hep-th/0312197] [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].
J.W. York, Jr., Role of conformal three geometry in the dynamics of gravitation, Phys. Rev. Lett. 28 (1972) 1082 [INSPIRE].
G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15 (1977) 2752 [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].
D.V. Fursaev and S.N. Solodukhin, On the description of the Riemannian geometry in the presence of conical defects, Phys. Rev. D 52 (1995) 2133 [hep-th/9501127] [INSPIRE].
D. Sarkar and M. Visser, The first law of differential entropy and holographic complexity, JHEP 11 (2020) 004 [arXiv:2008.12673] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
C. Núñez, A. Paredes and A.V. Ramallo, Unquenched flavor in the gauge/gravity correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
V. Balasubramanian and S.F. Ross, Holographic particle detection, Phys. Rev. D 61 (2000) 044007 [hep-th/9906226] [INSPIRE].
V. Balasubramanian et al., Thermalization of the spectral function in strongly coupled two dimensional conformal field theories, JHEP 04 (2013) 069 [arXiv:1212.6066] [INSPIRE].
D.M. McAvity and H. Osborn, Heat kernels for manifolds with boundary: applications to charged membranes, J. Phys. A 25 (1992) 3287 [INSPIRE].
D.M. McAvity, Surface energy from heat content asymptotics, J. Phys. A 26 (1993) 823 [INSPIRE].
R. Balian and C. Bloch, Distribution of eigenfrequencies for the wave equation in a finite domain. I. Three-dimensional problem with smooth boundary surface, Annals Phys. 60 (1970) 401 [INSPIRE].
R. Balian and C. Bloch, Distribution of eigenfrequencies for the wave equation in a finite domain. II. Electromagnetic field. Riemannian spaces, Annals Phys. 64 (1971) 271.
B. Duplantier, Exact curvature energies of charged membranes of arbitrary shapes, Physica A 168 (1990) 179.
E. Hijano, P. Kraus, E. Perlmutter and R. Snively, Witten diagrams revisited: the AdS geometry of conformal blocks, JHEP 01 (2016) 146 [arXiv:1508.00501] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, Dynamical structure and definition of energy in general relativity, Phys. Rev. 116 (1959) 1322 [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].
S.W. Hawking and G.T. Horowitz, The gravitational Hamiltonian, action, entropy and surface terms, Class. Quant. Grav. 13 (1996) 1487 [gr-qc/9501014] [INSPIRE].
J.M. Maldacena and L. Maoz, Wormholes in AdS, JHEP 02 (2004) 053 [hep-th/0401024] [INSPIRE].
T. Kawamoto, T. Mori, Y.-K. Suzuki, T. Takayanagi and T. Ugajin, Holographic local operator quenches in BCFTs, JHEP 05 (2022) 060 [arXiv:2203.03851] [INSPIRE].
L. Bianchi, S. De Angelis and M. Meineri, Radiation, entanglement and islands from a boundary local quench, arXiv:2203.10103 [INSPIRE].
Y. Kusuki, Semiclassical gravity from averaged boundaries in two-dimensional boundary conformal field theories, Phys. Rev. D 106 (2022) 066020 [arXiv:2206.03035] [INSPIRE].
Y. Kusuki and Z. Wei, AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles, arXiv:2210.03107 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
J.-M. Schlenker and E. Witten, No ensemble averaging below the black hole threshold, JHEP 07 (2022) 143 [arXiv:2202.01372] [INSPIRE].
J. Chandra, S. Collier, T. Hartman and A. Maloney, Semiclassical 3D gravity as an average of large-c CFTs, arXiv:2203.06511 [INSPIRE].
S.B. Giddings and A. Strominger, Axion induced topology change in quantum gravity and string theory, Nucl. Phys. B 306 (1988) 890 [INSPIRE].
S.R. Coleman, Black holes as red herrings: topological fluctuations and the loss of quantum coherence, Nucl. Phys. B 307 (1988) 867 [INSPIRE].
S.B. Giddings and A. Strominger, Loss of incoherence and determination of coupling constants in quantum gravity, Nucl. Phys. B 307 (1988) 854 [INSPIRE].
S. Giombi, A. Maloney and X. Yin, One-loop partition functions of 3D gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [INSPIRE].
Y.-K. Suzuki, One-loop correction to the AdS/BCFT partition function in three-dimensional pure gravity, Phys. Rev. D 105 (2022) 026023 [arXiv:2106.00206] [INSPIRE].
N. Benjamin, S. Collier and A. Maloney, Pure gravity and conical defects, JHEP 09 (2020) 034 [arXiv:2004.14428] [INSPIRE].
A. Maloney and E. Witten, Quantum gravity partition functions in three dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
C.A. Keller and A. Maloney, Poincaré series, 3D gravity and CFT spectroscopy, JHEP 02 (2015) 080 [arXiv:1407.6008] [INSPIRE].
N. Benjamin, H. Ooguri, S.-H. Shao and Y. Wang, Light-cone modular bootstrap and pure gravity, Phys. Rev. D 100 (2019) 066029 [arXiv:1906.04184] [INSPIRE].
M.R. Gaberdiel, B. Knighton and J. Vošmera, D-branes in AdS3 × S3 × T4 at k = 1 and their holographic duals, JHEP 12 (2021) 149 [arXiv:2110.05509] [INSPIRE].
A. Belin, S. Biswas and J. Sully, The spectrum of boundary states in symmetric orbifolds, JHEP 01 (2022) 123 [arXiv:2110.05491] [INSPIRE].
S. Chakraborty, K. Parattu and T. Padmanabhan, A novel derivation of the boundary term for the action in Lanczos-Lovelock gravity, Gen. Rel. Grav. 49 (2017) 121 [arXiv:1703.00624] [INSPIRE].
J. Jiang and H. Zhang, Surface term, corner term, and action growth in F(Rabcd) gravity theory, Phys. Rev. D 99 (2019) 086005 [arXiv:1806.10312] [INSPIRE].
O. Aharony, O. DeWolfe, D.Z. Freedman and A. Karch, Defect conformal field theory and locally localized gravity, JHEP 07 (2003) 030 [hep-th/0303249] [INSPIRE].
S. Cooper, M. Rozali, B. Swingle, M. Van Raamsdonk, C. Waddell and D. Wakeham, Black hole microstate cosmology, JHEP 07 (2019) 065 [arXiv:1810.10601] [INSPIRE].
D.E. Berenstein, R. Corrado, W. Fischler and J.M. Maldacena, The operator product expansion for Wilson loops and surfaces in the large N limit, Phys. Rev. D 59 (1999) 105023 [hep-th/9809188] [INSPIRE].
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Biswas, S., Kastikainen, J., Shashi, S. et al. Holographic BCFT spectra from brane mergers. J. High Energ. Phys. 2022, 158 (2022). https://doi.org/10.1007/JHEP11(2022)158
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DOI: https://doi.org/10.1007/JHEP11(2022)158