Abstract
In this paper, we obtain a bulk dual to the low energy sector of the SYK model, including SYK model with U(1) charge, by Kaluza-Klein (KK) reduction from three dimensions. We show that KK reduction of the 3D Einstein action plus its boundary term gives the Jackiw-Teitelboim (JT) model in 2D with the appropriate 1D boundary term. The size of the KK radius gets identified with the value of the dilaton in the resulting near-AdS2 geometry. In presence of U(1) charge, the 3D model additionally includes a U(1) Chern-Simons (CS) action. In order to describe a boundary theory with non-zero chemical potential, we also introduce a coupling between CS gauge field and bulk gravity. The 3D CS action plus the new coupling term with appropriate boundary terms reduce in two dimensions to a BF-type action plus a source term and boundary terms. The KK reduced 2D theory represents the soft sector of the charged SYK model. The pseudo-Nambu-Goldstone modes of combined Diff/SL(2, ℝ) and U(1)local/U(1) transformations are represented by combined large diffeomorphisms and large gauge transformations. The effective action of the former is reproduced by the action cost of the latter in the bulk dual, after appropriate identification of parameters. We compute chaotic correlators from the bulk and reproduce the result that the contribution from the “boundary photons” corresponds to zero Liapunov exponent.
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References
A. Dhar, G. Mandal and S.R. Wadia, Nonrelativistic fermions, coadjoint orbits of W(infinity) and string field theory at c = 1, Mod. Phys. Lett. A 7 (1992) 3129 [hep-th/9207011] [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].
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. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].
A. Kitaev, A simple model of quantum holography, talks at Kavli Institute for Theoretical Physics, Santa Barbara U.S.A. (2015).
S. Sachdev, Bekenstein-hawking entropy and strange metals, Phys. Rev. X 5 (2015) 041025.
J. Polchinski and V. Rosenhaus, The Spectrum in the Sachdev-Ye-Kitaev Model, JHEP 04 (2016) 001 [arXiv:1601.06768] [INSPIRE].
J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].
R. Gurau, The complete 1/N expansion of a SYK-like tensor model, Nucl. Phys. B 916 (2017) 386 [arXiv:1611.04032] [INSPIRE].
E. Witten, An SYK-Like Model Without Disorder, J. Phys. A 52 (2019) 474002 [arXiv:1610.09758] [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, W. Fu, A. Georges, Y. Gu, K. Jensen and S. Sachdev, Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev. B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].
A. Almheiri and J. Polchinski, Models of AdS2 backreaction and holography, JHEP 11 (2015) 014 [arXiv:1402.6334] [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.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].
M. Bañados, Three-dimensional quantum geometry and black holes, AIP Conf. Proc. 484 (1999) 147 [hep-th/9901148] [INSPIRE].
D.J. Gross and V. Rosenhaus, A Generalization of Sachdev-Ye-Kitaev, JHEP 02 (2017) 093 [arXiv:1610.01569] [INSPIRE].
D.J. Gross and V. Rosenhaus, All point correlation functions in SYK, JHEP 12 (2017) 148 [arXiv:1710.08113] [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].
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].
P. Nayak, A. Shukla, R.M. Soni, S.P. Trivedi and V. Vishal, On the Dynamics of Near-Extremal Black Holes, JHEP 09 (2018) 048 [arXiv:1802.09547] [INSPIRE].
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.
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].
T. Hartman and A. Strominger, Central Charge for AdS2 Quantum Gravity, JHEP 04 (2009) 026 [arXiv:0803.3621] [INSPIRE].
A. Castro, D. Grumiller, F. Larsen and R. McNees, Holographic Description of AdS2 Black Holes, JHEP 11 (2008) 052 [arXiv:0809.4264] [INSPIRE].
A. Castro and W. Song, Comments on AdS2 Gravity, arXiv:1411.1948 [INSPIRE].
M. Cvetǐc and I. Papadimitriou, AdS2 holographic dictionary, JHEP 12 (2016) 008 [Erratum ibid. 1701 (2017) 120] [arXiv:1608.07018] [INSPIRE].
T.G. Mertens, The Schwarzian theory — origins, JHEP 05 (2018) 036 [arXiv:1801.09605] [INSPIRE].
H.A. González, D. Grumiller and J. Salzer, Towards a bulk description of higher spin SYK, JHEP 05 (2018) 083 [arXiv:1802.01562] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS3/CFT2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
D. Stanford and E. Witten, Fermionic Localization of the Schwarzian Theory, JHEP 10 (2017) 008 [arXiv:1703.04612] [INSPIRE].
K. Bulycheva, A note on the SYK model with complex fermions, JHEP 12 (2017) 069 [arXiv:1706.07411] [INSPIRE].
G. Mandal, SYK model, Coadjoint orbits and Liouville bulk dual, talk given at YITP, Kyoto University, Kyoto Japan (2017), http://www2.yukawa.kyoto-u.ac.jp/∼tadashi.takayanagi/Mandal.pdf.
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].
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Dedicated to the memory of Joe Polchinski.
ArXiv ePrint: 1802.07746
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Gaikwad, A., Joshi, L.K., Mandal, G. et al. Holographic dual to charged SYK from 3D gravity and Chern-Simons. J. High Energ. Phys. 2020, 33 (2020). https://doi.org/10.1007/JHEP02(2020)033
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DOI: https://doi.org/10.1007/JHEP02(2020)033