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From Maldacena-Stanford 16:
Studies of holography have been hampered by the lack of a simple solvable model that can capture features of Einstein gravity. The simplest model, which is a single matrix quantum mechanics, does not appear to lead to black holes. $\mathcal{N} = 4$ super Yang Mills at strong ’t Hooft coupling certainly leads to black holes, and exact results are known at large N for many anomalous dimensions and some vacuum correlation functions, but at finite temperature the theory is difficult to study.
A system that reproduces some of the dynamics of black holes should be interacting, but we might hope for a model with interactions that are simple enough that it is still reasonable solvable.
Kitaev has proposed to study a quantum mechanical model of $N$ Majorana fermions interacting with random interactions (Kitaev 15). It is a simple variant of a model introduced by Sachdev and Ye (Sachdev-Ye 93), which was first discussed in relation to holography in (Sachdev 10).
From Maldacena 18:
The SYK model gives us a glimpse into the interior of an extremal black hole… That’s the feature of SYK that I find most interesting… It is a feature this model has, that I think no other model has
Let $\mathcal{J}_{i j k l}$ be random variables with expectation values $E[\mathcal{J}_{i j k l}]=0$ and $E[\mathcal{J}_{i j k l}^2]=\frac{6J^2}{N^3}$.
The Lagrangian density defining the SYK model is this:
The model is due to
Subir Sachdev, Jinwu Ye, Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet, Phys. Rev. Lett. 70:3339, 1993 (arXiv:cond-mat/9212030)
Alexei Kitaev, A simple model of quantum holography, Talks at KITP, April 7, 2015 and May 27, 2015. (part I, part II)
Textbook accounts:
Further review:
Subir Sachdev, The SYK model, talk at Aspen Center for Physics, 2018 (pdf)
Vladimir Rosenhaus, An introduction to the SYK model, Journal of Physics A: Mathematical and Theoretical, Volume 52, Number 32 (arXiv:1807.03334, doi:10.1088/1751-8121/ab2ce1)
Matteo Laudonio, Romain Pascalie, Adrian Tanasa, Combinatorial aspects of the Sachdev-Ye-Kitaev model (arXiv:2001.11849)
See also
Further developments:
Biao Lian, S. L. Sondhi, Zhenbin Yang, The chiral SYK model (arXiv:1906.03308)
Alexandre Streicher, SYK Correlators for All Energies (arxiv:1911.10171)
Relation to random matrix theory:
Discussion of possible realization of the SYK-model in condensed matter physics:
Relation of the SYK-model to the strange metals via AdS/CMT:
Discussion of the SYK-model as the AdS/CFT dual of JT-gravity in nearly AdS2/CFT1 and AdS-CFT in condensed matter physics:
Original articles:
Juan Maldacena, Douglas Stanford, Comments on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016)(arXiv:1604.07818)
Subir Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105:151602, 2010 (arXiv:1006.3794)
Review:
Gábor Sárosi, $AdS_2$ holography and the SYK model, Proceedings of Science 323 (arXiv:1711.08482, doi:10.22323/1.323.0001)
Juan Maldacena, Toy models for black holes II, talk at PiTP 2018 From QBits to spacetime (recording)
Dmitrii A. Trunin, Pedagogical introduction to SYK model and 2D Dilaton Gravity (arXiv:2002.12187)
Relation to black holes in terms of Majorana dimer states:
Relation to black holes in string theory and random matrix theory:
Jordan S. Cotler, Guy Gur-Ari, Masanori Hanada, Joseph Polchinski, Phil Saad, Stephen Shenker, Douglas Stanford, Alexandre Streicher, Masaki Tezuka, Black Holes and Random Matrices, JHEP 1705:118, 2017 (arXiv:1611.04650)
Tomoki Nosaka, Tokiro Numasawa, Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model (arXiv:1912.12302)
On non-perturbative effects and resurgence:
See also
Yuri D. Lensky, Xiao-Liang Qi, Pengfei Zhang, Size of bulk fermions in the SYK model (arXiv:2002.01961)
Xiao-Liang Qi, Pengfei Zhang, The Coupled SYK model at Finite Temperature (arXiv:2003.03916)
Akash Goel, Herman Verlinde, Towards a String Dual of SYK (arXiv:2103.03187)
Tarek Anous, Felix M. Haehl, The quantum $p$-spin glass model: A user manual for holographers (arXiv:2106.03838)
Discussion of (Lie algebra-)weight systems on chord diagrams encoding SYK model single trace observables:
(for more see at weight systems on chord diagrams in physics)
Antonio M. García-García, Yiyang Jia, Jacobus J. M. Verbaarschot, Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$, JHEP 04 (2018) 146 (arXiv:1801.02696)
Yiyang Jia, Jacobus J. M. Verbaarschot, Section 4 of: Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs, JHEP 11 (2018) 031 (arXiv:1806.03271)
Micha Berkooz, Prithvi Narayan, Joan Simón, Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction, JHEP 08 (2018) 192 (arxiv:1806.04380)
following:
which in turn follows
With emphasis on holographic content:
Micha Berkooz, Mikhail Isachenkov, Vladimir Narovlansky, Genis Torrents, Section 5 of: Towards a full solution of the large $N$ double-scaled SYK model, JHEP 03 (2019) 079 (arxiv:1811.02584)
Vladimir Narovlansky, Slide 23 (of 28) of: Towards a Solution of Large $N$ Double-Scaled SYK, 2019 (pdf)
and specifically in relation to Jackiw-Teitelboim gravity:
Andreas Blommaert, Thomas Mertens, Henri Verschelde, The Schwarzian Theory - A Wilson Line Perspective, JHEP 1812 (2018) 022 (arXiv:1806.07765)
Andreas Blommaert, Thomas Mertens, Henri Verschelde, Fine Structure of Jackiw-Teitelboim Quantum Gravity, JHEP 1909 (2019) 066 (arXiv:1812.00918)
Last revised on May 8, 2022 at 10:46:30. See the history of this page for a list of all contributions to it.