Bi-local holography in the SYK model: perturbations

Jevicki, Antal; Suzuki, Kenta

doi:10.1007/jhep11(2016)046

Cited by 144 publications

(193 citation statements)

References 42 publications

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“…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.

131

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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Section: Jhep06(2017)111mentioning

confidence: 99%

Supersymmetric SYK model and random matrix theory

Liu

Yuan

et al. 2017

J. High Energ. Phys.

131

147

View full text Add to dashboard Cite

show abstract

“…The Sachdev-Ye-Kitaev (SYK) model [1,2] has received much attention recently [3][4][5][6][7][8]. It is a simple model with solvable aspects which exhibits interesting connections to quantum chaos [9][10][11][12][13], black hole physics and quantum gravity in 1+1 dimensions [14][15][16][17][18][19][20].…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Higher dimensional generalizations of the SYK model

Berkooz

Narayan

Rozali

et al. 2017

J. High Energ. Phys.

142

127

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We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains N Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.

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“…The SYK model in the strong coupling limit has a maximal Lyapunov exponent [20,[23][24][25][26][27], a finite zero temperature entropy [20,21,28,29], a linear specific heat in the low temperature limit [30,31], the density of the low energy excitations grows exponentially [32][33][34][35] and short range spectral correlations are given by random matrix theory [33,36,37]. We note that the observation of a nonzero Lyapunov exponent at the Ehrenfest time and random matrix like level statistics at the Heisenberg time, a much larger time scale of the order of mean level spacing, are both signatures of quantum chaos.…”

Section: Introductionmentioning

confidence: 99%

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

2018

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We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, N Majorana fermions with infinite range interactions in 0 þ 1 dimensions. We have found that, close to the ground state E ≈ 0, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite N, which we compute analytically and numerically, grows exponentially with N for E ≈ 0. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above E ≈ 0, the spectral density grows exponentially with the energy. Deep in the quantum regime, corresponding to the first OðNÞ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for E ≈ 0 is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalue separations smaller than the Thouless energy, which seems to scale linearly with N. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universally characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor gðtÞ, obtained from the connected twolevel correlation function of the unfolded spectrum, decays as 1=t 2 for times shorter but comparable to the Thouless time with gð0Þ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

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Bi-local holography in the SYK model: perturbations

Cited by 144 publications

References 42 publications

Supersymmetric SYK model and random matrix theory

Supersymmetric SYK model and random matrix theory

Higher dimensional generalizations of the SYK model

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

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