Abstract
We analyse the dynamics of near-extremal Reissner-Nordström black holes in asymptotically four-dimensional Anti de Sitter space (AdS4). We work in the spherically symmetric approximation and study the thermodynamics and the response to a probe scalar field. We find that the behaviour of the system, at low energies and to leading order in our approximations, is well described by the Jackiw-Teitelboim (JT) model of gravity. In fact, this behaviour can be understood from symmetry considerations and arises due to the breaking of time reparametrisation invariance. The JT model has been analysed in considerable detail recently and related to the behaviour of the SYK model. Our results indicate that features in these models which arise from symmetry considerations alone are more general and present quite universally in near-extremal black holes.
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References
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].
A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).
A. Jevicki, K. Suzuki and J. Yoon, Bi-local holography in the SYK model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].
Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP 05 (2017) 125 [arXiv:1609.07832] [INSPIRE].
D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher dimensional generalizations of the SYK model, JHEP 01 (2017) 138 [arXiv:1610.02422] [INSPIRE].
A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].
W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].
E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].
R. Gurau, The complete 1/N expansion of a SYK-like tensor model, Nucl. Phys. B 916 (2017) 386 [arXiv:1611.04032] [INSPIRE].
I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
R.A. Davison et al., Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum chaos and holographic tensor models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].
T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP 06 (2017) 111 [arXiv:1702.01738] [INSPIRE].
J. Murugan, D. Stanford and E. Witten, More on Supersymmetric and 2d Analogs of the SYK Model, JHEP 08 (2017) 146 [arXiv:1706.05362] [INSPIRE].
D.J. Gross and V. Rosenhaus, A line of CFTs: from generalized free fields to SYK, JHEP 07 (2017) 086 [arXiv:1706.07015] [INSPIRE].
K. Bulycheva, A note on the SYK model with complex fermions, JHEP 12 (2017) 069 [arXiv:1706.07411] [INSPIRE].
A. Gaikwad and R. Sinha, Spectral form factor in non-gaussian random matrix theories, arXiv:1706.07439 [INSPIRE].
A. Eberlein, V. Kasper, S. Sachdev and J. Steinberg, Quantum quench of the Sachdev-Ye-Kitaev model, Phys. Rev. B 96 (2017) 205123 [arXiv:1706.07803] [INSPIRE].
J. Yoon, SYK models and SYK-like tensor models with global symmetry, JHEP 10 (2017) 183 [arXiv:1707.01740] [INSPIRE].
J. Sonner and M. Vielma, Eigenstate thermalization in the Sachdev-Ye-Kitaev model, JHEP 11 (2017) 149 [arXiv:1707.08013] [INSPIRE].
S. Choudhury et al., Notes on melonic O(N)q − 1 tensor models, JHEP 06 (2018) 094 [arXiv:1707.09352] [INSPIRE].
C. Krishnan, K.V. Pavan Kumar and D. Rosa, Contrasting SYK-like models, JHEP 01 (2018) 064 [arXiv:1709.06498] [INSPIRE].
R. Bhattacharya, S. Chakrabarti, D.P. Jatkar and A. Kundu, SYK model, chaos and conserved charge, JHEP 11 (2017) 180 [arXiv:1709.07613] [INSPIRE].
S. Förste, J. Kames-King and M. Wiesner, Towards the holographic dual of N = 2 SYK, JHEP 03 (2018) 028 [arXiv:1712.07398] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
S.H. Shenker and D. Stanford, Stringy effects in scrambling, JHEP 05 (2015) 132 [arXiv:1412.6087] [INSPIRE].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic description of AdS 2 black holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
A. Castro and W. Song, Comments on AdS 2 gravity, arXiv:1411.1948 [INSPIRE].
K. Jensen, Chaos in AdS 2 holography, Phys. Rev. Lett. 117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].
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].
J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2 backreaction and holography, JHEP 07 (2016) 139 [arXiv:1606.03438] [INSPIRE].
A. Almheiri and B. Kang, Conformal symmetry breaking and thermodynamics of near-extremal black holes, JHEP 10 (2016) 052 [arXiv:1606.04108] [INSPIRE].
M. Cvetič and I. Papadimitriou, AdS 2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, JHEP 11 (2017) 046 [arXiv:1702.04266] [INSPIRE].
D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP 05 (2017) 092 [arXiv:1702.08016] [INSPIRE].
S. Förste and I. Golla, Nearly AdS 2 SUGRA and the super-Schwarzian, Phys. Lett. B 771 (2017) 157 [arXiv:1703.10969] [INSPIRE].
S.R. Das, A. Jevicki and K. Suzuki, Three dimensional view of the SYK/AdS duality, JHEP 09 (2017) 017 [arXiv:1704.07208] [INSPIRE].
H. Kyono, S. Okumura and K. Yoshida, Comments on 2D dilaton gravity system with a hyperbolic dilaton potential, Nucl. Phys. B 923 (2017) 126 [arXiv:1704.07410] [INSPIRE].
C. Eling, Holography and AdS 2 gravity with a dynamical aether, JHEP 07 (2017) 147 [arXiv:1705.04334] [INSPIRE].
S. Dartois, H. Erbin and S. Mondal, Conformality of 1/N corrections in SYK-like models, arXiv:1706.00412 [INSPIRE].
C. Krishnan and K.V.P. Kumar, Towards a finite-N hologram, JHEP 10 (2017) 099 [arXiv:1706.05364] [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
P. Caputa et al., Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT, JHEP 11 (2017) 097 [arXiv:1706.07056] [INSPIRE].
M. Taylor, Generalized conformal structure, dilaton gravity and SYK, JHEP 01 (2018) 010 [arXiv:1706.07812] [INSPIRE].
D. Grumiller et al., Menagerie of AdS 2 boundary conditions, JHEP 10 (2017) 203 [arXiv:1708.08471] [INSPIRE].
J. de Boer, E. Llabrés, J.F. Pedraza and D. Vegh, Chaotic strings in AdS/CFT, Phys. Rev. Lett. 120 (2018) 201604 [arXiv:1709.01052] [INSPIRE].
S.-K. Jian, Z.-Y. Xian and H. Yao, Quantum criticality and duality in the Sachdev-Ye-Kitaev/AdS 2 chain, Phys. Rev. B 97 (2018) 205141 [arXiv:1709.02810] [INSPIRE].
R.-G. Cai, S.-M. Ruan, R.-Q. Yang and Y.-L. Zhang, The string worldsheet as the holographic dual of SYK state, arXiv:1709.06297 [INSPIRE].
N. Halmagyi and S. Mondal, Tensor models for black hole probes, arXiv:1711.04385 [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Three dimensional view of arbitrary q SYK models, JHEP 02 (2018) 162 [arXiv:1711.09839] [INSPIRE].
S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Space-Time in the SYK model, JHEP 07 (2018) 184 [arXiv:1712.02725] [INSPIRE].
F.M. Haehl and M. Rozali, Fine grained chaos in AdS 2 gravity, Phys. Rev. Lett. 120 (2018) 121601 [arXiv:1712.04963] [INSPIRE].
T.G. Mertens, The Schwarzian theory — Origins, JHEP 05 (2018) 036 [arXiv:1801.09605] [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].
C. Teitelboim, Gravitation and hamiltonian structure in two space-time dimensions, Phys. Lett. B 126 (1983) 41.
R. Jackiw, Lower dimensional gravity, Nucl. Phys. B 252 (1985) 343.
A. Almheiri and J. Polchinski, Models of AdS 2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [INSPIRE].
A. Gaikwad, L.K. Joshi, G. Mandal and S.R. Wadia, Holographic dual to charged SYK from 3D gravity and Chern-Simons, arXiv:1802.07746 [INSPIRE].
H.J. Boonstra, K. Skenderis and P.K. Townsend, The domain wall/QFT correspondence, JHEP 01 (1999) 003 [hep-th/9807137] [INSPIRE].
K. Skenderis and M. Taylor, Kaluza-Klein holography, JHEP 05 (2006) 057 [hep-th/0603016] [INSPIRE].
B. Gouteraux, J. Smolic, M. Smolic, K. Skenderis and M. Taylor, Holography for Einstein-Maxwell-dilaton theories from generalized dimensional reduction, JHEP 01 (2012) 089 [arXiv:1110.2320] [INSPIRE].
A.D. Shapere, S. Trivedi and F. Wilczek, Dual dilaton dyons, Mod. Phys. Lett. A 6 (1991) 2677 [INSPIRE].
J.M. Maldacena and L. Susskind, D-branes and fat black holes, Nucl. Phys. B 475 (1996) 679 [hep-th/9604042] [INSPIRE].
M. Henningson and K. Skenderis, Holography and the Weyl anomaly, Fortsch. Phys. 48 (2000) 125 [hep-th/9812032] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [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].
R.B. Mann, Entropy of rotating Misner string space-times, Phys. Rev. D 61 (2000) 084013 [hep-th/9904148] [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].
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].
H. Liu and A.A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097] [INSPIRE].
D.A. Roberts and D. Stanford, Two-dimensional conformal field theory and the butterfly effect, Phys. Rev. Lett. 115 (2015) 131603 [arXiv:1412.5123] [INSPIRE].
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Nayak, P., Shukla, A., Soni, R.M. et al. On the dynamics of near-extremal black holes. J. High Energ. Phys. 2018, 48 (2018). https://doi.org/10.1007/JHEP09(2018)048
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DOI: https://doi.org/10.1007/JHEP09(2018)048