Abstract
We have recently presented a geometry dual to a Schwinger-Keldysh closed time contour, with two equal β/2 length Euclidean sections, which can be thought of as dual to the Thermo Field Dynamics formulation of the boundary CFT. In this work we study non-perturbative holographic excitations of the thermal vacuum by turning on asymptotic Euclidean sources. In the large-N approximation the states are found to be thermal coherent states and we manage to compute its eigenvalues. We pay special attention to the high temperature regime where the manifold is built from pieces of Euclidean and Lorentzian black hole geometries. In this case, the real time segments of the Schwinger-Keldysh contour get connected by an Einstein-Rosen wormhole through the bulk, which we identify as the exterior of a single maximally extended black hole. The Thermal-AdS case is also considered but, the Lorentzian regions become disconnected, its results mostly follows from the zero temperature case.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
D. Marolf, States and boundary terms: subtleties of Lorentzian AdS/CFT, JHEP 05 (2005) 042 [hep-th/0412032] [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality, Phys. Rev. Lett. 101 (2008) 081601 [arXiv:0805.0150] [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
M. Botta-Cantcheff, P. Martínez and G.A. Silva, On excited states in real-time AdS/CFT, JHEP 02 (2016) 171 [arXiv:1512.07850] [INSPIRE].
A. Christodoulou and K. Skenderis, Holographic construction of excited CFT states, JHEP 04 (2016) 096 [arXiv:1602.02039] [INSPIRE].
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [INSPIRE].
M. Botta-Cantcheff, P.J. Martínez and G.A. Silva, Interacting fields in real-time AdS/CFT, JHEP 03 (2017) 148 [arXiv:1703.02384] [INSPIRE].
A. Lewkowycz and O. Parrikar, The holographic shape of entanglement and Einstein’s equations, JHEP 05 (2018) 147 [arXiv:1802.10103] [INSPIRE].
A. May and E. Hijano, The holographic entropy zoo, JHEP 10 (2018) 036 [arXiv:1806.06077] [INSPIRE].
D. Marolf, Microcanonical path integrals and the holography of small black hole interiors, JHEP 09 (2018) 114 [arXiv:1808.00394] [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement II: It from BC-bit, arXiv:1809.01197 [INSPIRE].
J. Sonner and B. Withers, Linear gravity from conformal symmetry, arXiv:1810.12923 [INSPIRE].
A. Belin, A. Lewkowycz and G. Sárosi, Complexity and the bulk volume, a New York time story, JHEP 03 (2019) 044 [arXiv:1811.03097] [INSPIRE].
M. Botta-Cantcheff, P.J. Martínez and G.A. Silva, The gravity dual of real-time CFT at finite temperature, JHEP 11 (2018) 129 [arXiv:1808.10306] [INSPIRE].
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [INSPIRE].
H. Umezawa, Advanced field theory: Micro, macro, and thermal physics, AIP, New York U.S.A. (1993).
Y. Takahashi and H. Umezawa, Thermo field dynamics, Int. J. Mod. Phys. B 10 (1996) 1755 [INSPIRE].
J.M. Maldacena, Eternal black holes in Anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
B.C. van Rees, Real-time gauge/gravity duality and ingoing boundary conditions, Nucl. Phys. Proc. Suppl. 192-193 (2009) 193 [arXiv:0902.4010] [INSPIRE].
A. Belin, A. Lewkowycz and G. Sárosi, The boundary dual of the bulk symplectic form, Phys. Lett. B 789 (2019) 71 [arXiv:1806.10144] [INSPIRE].
J. Oz-Vogt, A. Mann and M. Revzen, Thermal coherent states and thermal squeezed states, J. Mod. Opt. 38 (1991) 2339.
S. Fubini, A.J. Hanson and R. Jackiw, New approach to field theory, Phys. Rev. D 7 (1973) 1732.
T. Faulkner et al., Nonlinear gravity from entanglement in conformal field theories, JHEP 08 (2017) 057 [arXiv:1705.03026] [INSPIRE].
D. Marolf et al., From Euclidean sources to lorentzian spacetimes in holographic conformal field theories, JHEP 06 (2018) 077 [arXiv:1709.10101] [INSPIRE].
M. Botta-Cantcheff and P.J. Martínez, Which quantum states are dual to classical spacetimes?, arXiv:1703.03483 [INSPIRE].
B. Mosk, Metric perturbations of extremal surfaces, Class. Quant. Grav. 35 (2018) 045013 [arXiv:1710.01316] [INSPIRE].
J.B. Hartle and S.W. Hawking, Wave function of the universe, Phys. Rev. D 28 (1983) 2960.
A.L. Fitzpatrick and J. Kaplan, Scattering states in AdS/CFT, arXiv:1104.2597 [INSPIRE].
H. Matsumoto et al., Thermo field dynamics in interaction representation, Prog. Theor. Phys. 70 (183) 599.
T. Hartman and J. Maldacena, Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [arXiv:1303.1080] [INSPIRE].
K. Papadodimas and S. Raju, Remarks on the necessity and implications of state-dependence in the black hole interior, Phys. Rev. D 93 (2016) 084049 [arXiv:1503.08825] [INSPIRE].
A. Maloney, Geometric microstates for the three dimensional black hole?, arXiv:1508.04079 [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. D 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].
E. D’Hoker and D.Z. Freedman, Supersymmetric gauge theories and the AdS/CFT correspondence, hep-th/0201253 [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
D.T. Son and A.O. Starinets, Viscosity, black holes and quantum field theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].
D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasinormal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [INSPIRE].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
P. Glorioso, M. Crossley and H. Liu, A prescription for holographic Schwinger-Keldysh contour in non-equilibrium systems, arXiv:1812.08785 [INSPIRE].
D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFT d /AdS d+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].
D. Birmingham, I. Sachs and S.N. Solodukhin, Relaxation in conformal field theory, Hawking-Page transition and quasinormal normal modes, Phys. Rev. D 67 (2003) 104026 [hep-th/0212308] [INSPIRE].
A. Einstein and N. Rosen, The particle problem in the general theory of relativity, Phys. Rev. 48 (1935) 73 [INSPIRE].
M. Kenmoku, M. Kuwata and K. Shigemoto, Normal modes and no zero mode theorem of scalar fields in BTZ black hole spacetime, Class. Quant. Grav. 25 (2008) 145016 [arXiv:0801.2044] [INSPIRE].
S. Hemming and E. Keski-Vakkuri, Hawking radiation from AdS black holes, Phys. Rev. D 64 (2001) 044006 [gr-qc/0005115] [INSPIRE].
D. Harlow and D. Stanford, Operator dictionaries and wave functions in AdS/CFT and dS/CFT, arXiv:1104.2621 [INSPIRE].
W.-M. Zhang, D.H. Feng and R. Gilmore, Coherent states: theory and some applications, Rev. Mod. Phys. 62 (1990) 867 [INSPIRE].
A. Belin, N. Iqbal and S.F. Lokhande, Bulk entanglement entropy in perturbative excited states, SciPost Phys. 5 (2018) 024 [arXiv:1805.08782] [INSPIRE].
S.M. Carroll, Spacetime and geometry: an introduction to general relativity, Addison-Wesley, San Francisco, U.S.A. (2004).
M.C.B. Abdalla, A.L. Gadelha and D.L. Nedel, Closed string thermal torus from thermofield dynamics, Phys. Lett. B 613 (2005) 213 [hep-th/0410068].
M. Botta Cantcheff, D-branes as coherent states in the open string channel, Eur. Phys. J. C 55 (2008) 517 [arXiv:0710.3186] [INSPIRE].
J.J. Bisognano and E.H. Wichmann, On the duality condition for a hermitian scalar field, J. Math. Phys. 16 (1975) 985 [INSPIRE].
J.J. Bisognano and E.H. Wichmann, On the duality condition for quantum fields, J. Math. Phys. 17 (1976) 303 [INSPIRE].
R.E. Arias, M. Botta Cantcheff and G.A. Silva, Lorentzian AdS, wormholes and holography, Phys. Rev. D 83 (2011) 066015 [arXiv:1012.4478] [INSPIRE].
P. Gao, D.L. Jafferis and A. Wall, Traversable wormholes via a double trace deformation, JHEP 12 (2017) 151 [arXiv:1608.05687] [INSPIRE].
M. Botta Cantcheff, A.L. Gadelha, D.F.Z. Marchioro and D.L. Nedel, Entanglement from dissipation and Holographic Interpretation, Eur. Phys. J. C 78 (2018) 105 [arXiv:1702.02069] [INSPIRE].
J. Maldacena, S.H. Shenker and D. Stanford, A bound on chaos, JHEP 08 (2016) 106 [arXiv:1503.01409] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1901.00505
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Botta-Cantcheff, M., Martínez, P.J. & Silva, G.A. Holographic excited states in AdS black holes. J. High Energ. Phys. 2019, 28 (2019). https://doi.org/10.1007/JHEP04(2019)028
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2019)028