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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:
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)
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)
Further developments in
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:
See also
Discussion of possible realization of the SYK-model in condensed matter physics:
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)
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)
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 5, 2021 at 12:32:31. See the history of this page for a list of all contributions to it.