Contrasting SYK-like models

Krishnan, Chethan; Kumar, K. Vinod; Rosa, Dario

doi:10.1007/jhep01(2018)064

Cited by 49 publications

(47 citation statements)

References 80 publications

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“…Tensor models were initially studied in zero dimension in the context of quantum gravity and random geometry [3,[14][15][16][17]. They were then studied in one dimension [18][19][20][21][22][23][24][25][26][27][28][29][30] (see also [4,31] for reviews) as a generalization of the Sachdev-Ye-Kitaev model [32][33][34][35][36][37] without quenched disorder.…”

Section: Introductionmentioning

confidence: 99%

Hints of unitarity at large N in the O(N )3 tensor field theory

Benedetti

Gurău

Harribey

et al. 2020

J. High Energ. Phys.

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We compute the OPE coefficients of the bosonic tensor model of [1] for three point functions with two fields and a bilinear with zero and non-zero spin. We find that all the OPE coefficients are real in the case of an imaginary tetrahedral coupling constant, while one of them is not real in the case of a real coupling. We also discuss the operator spectrum of the free theory based on the character decomposition of the partition function.

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Section: Introductionmentioning

confidence: 99%

Hints of unitarity at large N in the O(N )3 tensor field theory

Benedetti

Gurău

Harribey

et al. 2020

J. High Energ. Phys.

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“…are two mutually orthogonal projectors which span the interaction space. 18 We parametrize the interaction in terms of λ 1 = λp 3 and λ 2 = λ d + λ p . Thus, the four-point kernel in momentum space becomes:…”

Section: The Four-point Couplingsmentioning

confidence: 99%

“…Tensor models have been extensively studied in zero dimensions (where they were originally introduced as models of quantum gravity [10,11], and further studied with similar motivation [12,2,13]) and in one dimension (e.g. [14,15,1,16,17,18,19,20,21,22,23], see also [24,4] for reviews) as they provide an alternative to the Sachdev-Ye-Kitaev model [25,26,27,28,29] dispensing with the quenched disorder of the latter.…”

Section: Introductionmentioning

confidence: 99%

Line of fixed points in a bosonic tensor model

Benedetti

Gurău

Harribey

2019

J. High Energ. Phys.

149

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We consider the O(N ) 3 tensor model of Klebanov and Tarnopolsky [1] in d < 4 with a free covariance modified to fit the infrared conformal scaling. We study the renormalization group flow of the model using a Wilsonian approach valid in any d (notably we do not require d = 4 − with small ). At large N , the tetrahedral coupling has a finite flow, hence it becomes a free parameter. The remaining flow can be parameterized by two couplings which do not mix. We show that, at leading order in 1/N but non perturbatively in the couplings, the beta functions stop at quadratic order in the pillow and double-trace couplings. We find four fixed points which depend parametrically on the tetrahedral coupling. For purely imaginary values of the latter we identify a real and infrared attractive fixed point. We remark that an imaginary tetrahedral coupling is in fact natural from the onset as the tetrahedral invariant does not have any positivity property, and moreover in the large-N limit the beta functions depend on the square of the tetrahedral coupling, thus they remain real, as long as the other couplings stay real.

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“…Recently, different extensions of the SYK model have been studied including several fermionic flavors [42,43], higher dimensions [44][45][46][47][48], one plus two-body interactions [49][50][51], with supersymmetry [52][53][54][55][56][57][58][59] and with no disorder [37,60,61].…”

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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Contrasting SYK-like models

Cited by 49 publications

References 80 publications

Hints of unitarity at large N in the O(N )3 tensor field theory

Hints of unitarity at large N in the O(N )3 tensor field theory

Line of fixed points in a bosonic tensor model

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

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