Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex

doi:10.1016/j.nuclphysb.2016.08.002

Cited by 289 publications

(464 citation statements)

References 17 publications

(65 reference statements)

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“…However, the dilaton is not constant and has a nontrivial action, of the type studied in [3]. It was recognized in [38,39] (see also [40][41][42][43]) that this…”

Section: Fermion Four-point Functionmentioning

confidence: 99%

The bulk dual of SYK: cubic couplings

Gross

Rosenhaus

2017

J. High Energ. Phys.

155

200

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The SYK model, a quantum mechanical model of N 1 Majorana fermions χ i , with a q-body, random interaction, is a novel realization of holography. It is known that the AdS 2 dual contains a tower of massive particles, yet there is at present no proposal for the bulk theory. As SYK is solvable in the 1/N expansion, one can systematically derive the bulk. We initiate such a program, by analyzing the fermion two, four and six-point functions, from which we extract the tower of singlet, large N dominant, operators, their dimensions, and their three-point correlation functions. These determine the masses of the bulk fields and their cubic couplings. We present these couplings, analyze their structure and discuss the simplifications that arise for large q.

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“…However, the dilaton is not constant and has a nontrivial action, of the type studied in [3]. It was recognized in [38,39] (see also [40][41][42][43]) that this…”

Section: Fermion Four-point Functionmentioning

confidence: 99%

The bulk dual of SYK: cubic couplings

Gross

Rosenhaus

2017

J. High Energ. Phys.

155

200

View full text Add to dashboard Cite

show abstract

“…SYK model [6][7][8][9][10] is a microscopic quantum hamiltonian with random Gaussian non-local couplings among majonara fermions. As is maximally chaotic and nearly conformal, this model could be treated as a holographic dual of quantum black hole with AdS 2 horizon through the (near) AdS/CFT correspondence [11][12][13][14][15][16][17][18][19][20]. In the recent research people have also discussed several generalizations of the SYK model [21][22][23][24], such as higher dimensional generalizations and supersymmetric constraints.…”

Section: Jhep06(2017)111mentioning

confidence: 99%

Supersymmetric SYK model and random matrix theory

Liu

Yuan

et al. 2017

J. High Energ. Phys.

130

147

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In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N = 1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the spectral form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.

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“…Majorana fermions in zero spatial dimensions with q−body infinite-range random interactions in Fock space, commonly termed Sachdev-Ye-Kitaev (SYK) models [1][2][3][4][5][6][7][8][9][10][11], are attracting a great deal of attention as one of the simplest strongly interacting system with a gravity dual [12]. Previously, a closely related model with Majorana fermions replaced by Dirac fermions at finite chemical potential was intensively investigated in nuclear physics [13][14][15][16][17][18] and later in the study of spin-liquids [19].…”

Section: Introductionmentioning

confidence: 99%

Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N

2017

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We derive an approximate analytical formula for the spectral density of the q-body This spectral density reproduces the known result for the free energy in the large q and N limit at arbitrary values of the temperature. In the infrared region, where the SachdevYe-Kitaev model is believed to have a gravity-dual, the analytical spectral density is given. It therefore has a square-root edge, as in random matrix ensembles, followed by an exponential growth, a distinctive feature of black holes and also of low energy nuclear excitations. Results for level-statistics in this region confirm the agreement with random matrix theory. Physically this is a signature that, for sufficiently long times, the SYK model and its gravity dual evolve to a fully ergodic state whose dynamics only depends on the global symmetry of the system. Our results strongly suggest that random matrix correlations are a universal feature of quantum black holes and that the SYK model, combined with holography, may be relevant to model certain aspects of the nuclear dynamics.

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Sachdev–Ye–Kitaev model as Liouville quantum mechanics

Cited by 289 publications

References 17 publications

The bulk dual of SYK: cubic couplings

The bulk dual of SYK: cubic couplings

Supersymmetric SYK model and random matrix theory

Analytical spectral density of the Sachdev-Ye-Kitaev model at finite N

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