Abstract
Conformal field theories can exchange energy through a boundary interface. Imposing conformal boundary conditions for static interfaces implies energy conservation at the interface. Recently, the reflective and transmittive properties of such static conformal interfaces have been studied in two dimensions by scattering matter at the interface impurity. In this note, we generalize this to the case of dynamic interfaces. Motivated by the connections between the moving mirror and the black hole, we choose a particular profile for the dynamical interface. We show that a part of the total energy of each side will be lost in the interface. In other words, a time-dependent interface can accumulate or absorb energy. While, in general, the interface follows a time-like trajectory, one can take a particular limit of a profile parameter(β), such that the interface approaches a null line asymptotically(β → 0). In this limit, we show that for a class of boundary conditions, the interface behaves like a semipermeable membrane - it behaves like a (partially) reflecting mirror from one side and is (partially) transparent from the other side. We also consider another set of conformal boundary conditions for which, in the null line limit, the interface mimics the properties expected of a horizon. In this case, we devise a scattering experiment, where (zero-point subtracted) energy from one CFT is fully transmitted to the other CFT, while from the other CFT, energy can neither be transmitted nor reflected, i.e., it gets lost in the interface. This boundary condition is also responsible for the thermal energy spectrum which mimics Hawking radiation. This is analogous to the black hole where the horizon plays the role of a one-sided ‘membrane’, which accumulates all the interior degrees of freedom and radiates thermally in the presence of quantum fluctuation. Stimulated by this observation, we comment on some plausible construction of wormhole analogues.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Calabrese and J. Cardy, Quantum quenches in 1 + 1 dimensional conformal field theories, J. Stat. Mech. 1606 (2016) 064003 [arXiv:1603.02889] [INSPIRE].
P.C.W. Davies and S.A. Fulling, Radiation from a moving mirror in two-dimensional space-time conformal anomaly, Proc. Roy. Soc. Lond. A 348 (1976) 393 [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge Univ. Press, Cambridge, U.K. (1984) [https://doi.org/10.1017/CBO9780511622632] [INSPIRE].
R.D. Carlitz and R.S. Willey, Reflections on moving mirrors, Phys. Rev. D 36 (1987) 2327 [INSPIRE].
S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
J.L. Cardy, Conformal invariance and surface critical behavior, Nucl. Phys. B 240 (1984) 514 [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].
I. Akal et al., Holographic moving mirrors, Class. Quant. Grav. 38 (2021) 224001 [arXiv:2106.11179] [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].
J. Basak Kumar et al., Reflected entropy and entanglement negativity for holographic moving mirrors, JHEP 09 (2022) 089 [arXiv:2204.06015] [INSPIRE].
M.R.R. Good, A. Lapponi, O. Luongo and S. Mancini, Quantum communication through a partially reflecting accelerating mirror, Phys. Rev. D 104 (2021) 105020 [arXiv:2103.07374] [INSPIRE].
T. Quella, I. Runkel and G.M.T. Watts, Reflection and transmission for conformal defects, JHEP 04 (2007) 095 [hep-th/0611296] [INSPIRE].
M. Meineri, J. Penedones and A. Rousset, Colliders and conformal interfaces, JHEP 02 (2020) 138 [arXiv:1904.10974] [INSPIRE].
D.M. Hofman and J. Maldacena, Conformal collider physics: energy and charge correlations, JHEP 05 (2008) 012 [arXiv:0803.1467] [INSPIRE].
V. Papadopoulos, Membranes, holography, and quantum information, arXiv:2310.18521 [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960 [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [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].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
T. Hartman, Lectures on quantum gravity and black holes, http://www.hartmanhep.net/topics2015/gravity-lectures.pdf.
A. Kundu, Wormholes and holography: an introduction, Eur. Phys. J. C 82 (2022) 447 [arXiv:2110.14958] [INSPIRE].
R. Haag, Local quantum physics, Springer, Berlin, Germany (1996) [https://doi.org/10.1007/978-3-642-61458-3] [INSPIRE].
E. Witten, APS medal for exceptional achievement in research: invited article on entanglement properties of quantum field theory, Rev. Mod. Phys. 90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].
L.C.B. Crispino, A. Higuchi and G.E.A. Matsas, The Unruh effect and its applications, Rev. Mod. Phys. 80 (2008) 787 [arXiv:0710.5373] [INSPIRE].
S.B. Giddings and W.M. Nelson, Quantum emission from two-dimensional black holes, Phys. Rev. D 46 (1992) 2486 [hep-th/9204072] [INSPIRE].
L. Susskind, Computational complexity and black hole horizons, Fortsch. Phys. 64 (2016) 24 [arXiv:1403.5695] [INSPIRE].
L. Susskind, Entanglement is not enough, Fortsch. Phys. 64 (2016) 49 [arXiv:1411.0690] [INSPIRE].
L. Susskind, Three lectures on complexity and black holes, arXiv:1810.11563 [INSPIRE].
Y. Sato, Complexity in a moving mirror model, Phys. Rev. D 105 (2022) 086016 [arXiv:2108.04637] [INSPIRE].
S. Chapman, D. Ge and G. Policastro, Holographic complexity for defects distinguishes action from volume, JHEP 05 (2019) 049 [arXiv:1811.12549] [INSPIRE].
Y. Sato and K. Watanabe, Does boundary distinguish complexities?, JHEP 11 (2019) 132 [arXiv:1908.11094] [INSPIRE].
P. Braccia, A.L. Cotrone and E. Tonni, Complexity in the presence of a boundary, JHEP 02 (2020) 051 [arXiv:1910.03489] [INSPIRE].
S. Baiguera, S. Bonansea and K. Toccacelo, Volume complexity for the nonsupersymmetric Janus AdS5 geometry, Phys. Rev. D 104 (2021) 086030 [arXiv:2105.12743] [INSPIRE].
R. Auzzi, S. Baiguera, S. Bonansea and G. Nardelli, Action complexity in the presence of defects and boundaries, JHEP 02 (2022) 118 [arXiv:2112.03290] [INSPIRE].
M. Gutperle and J.D. Miller, Entanglement entropy at holographic interfaces, Phys. Rev. D 93 (2016) 026006 [arXiv:1511.08955] [INSPIRE].
K. Sakai and Y. Satoh, Entanglement through conformal interfaces, JHEP 12 (2008) 001 [arXiv:0809.4548] [INSPIRE].
A. Karch et al., Universality of effective central charge in interface CFTs, JHEP 11 (2023) 126 [arXiv:2308.05436] [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].
C. Bachas et al., Energy transport for thick holographic branes, Phys. Rev. Lett. 131 (2023) 021601 [arXiv:2212.14058] [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].
V. Burman, S. Das and C. Krishnan, A smooth horizon without a smooth horizon, JHEP 03 (2024) 014 [arXiv:2312.14108] [INSPIRE].
C. Krishnan and P.S. Pathak, Normal modes of the stretched horizon: a bulk mechanism for black hole microstate level spacing, JHEP 03 (2024) 162 [arXiv:2312.14109] [INSPIRE].
S. Banerjee, S. Das, M. Dorband and A. Kundu, Brickwall, normal modes and emerging thermality, arXiv:2401.01417 [INSPIRE].
D. Marolf and J. Polchinski, Gauge/gravity duality and the black hole interior, Phys. Rev. Lett. 111 (2013) 171301 [arXiv:1307.4706] [INSPIRE].
C. Krishnan, Lectures on quantum black holes, https://www.youtube.com/playlist?list=PL0Xu0_GJeFY7D01dGq-CINS261zG-8yru.
M. Miyaji, S. Ryu, T. Takayanagi and X. Wen, Boundary states as holographic duals of trivial spacetimes, JHEP 05 (2015) 152 [arXiv:1412.6226] [INSPIRE].
Acknowledgments
We would like to thank Vaibhav Burman, Justin David, Bobby Ezhuthachan, Dongsheng Ge, Chethan Krishnan, Somnath Porey, Koushik Ray, Baishali Roy and Tadashi Takayanagi for useful related discussions. We would like to thank Baishali and Somnath for collaborating with us at the initial stage of the project. We are especially grateful to Bobby for introducing us to ICFT as well as for suggesting us one of the key problems of this project. We thank him for his constant support and encouragement throughout this work and for clarifying some key points of this work. We also thank him for reading our draft carefully and suggesting some conceptual changes therein. We would also like to thank the Physics Department of RKMVERI as well as the organizers of the Workshop on ‘Ergodicity and its breaking: a view from Many Body, QFT and Holography’ at RKMVERI, where this project was discussed and initiated. AD and SD would like to thank the hospitality of the Physics department, RKMVERI while visiting there in the course of this project. We would also like to thank Chethan Krishnan for the course on ‘Quantum Black Holes’ [47] at CHEP, IISC, which proved to be helpful and illuminating in getting a key motivation on some part of the project. AD would like to thank Tadashi Takayanagi for useful in-person discussion during The Kavli Asian Winter School, 2023, in Kyoto and he would also like to thank the organizers of the school for giving him an opportunity to present some part of this work. PB would like to acknowledge the support provided by the grant CRG/2021/004539. The research work of SD is supported by a DST Inspire Faculty Fellowship.
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: 2401.11451
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
Biswas, P., Das, S. & Dinda, A. Moving interfaces and two-dimensional black holes. J. High Energ. Phys. 2024, 329 (2024). https://doi.org/10.1007/JHEP05(2024)329
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)329