Conformality of 
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 corrections in Sachdev-Ye-Kitaev-like models

Dartois, Stephane; Erbin, Harold; Mondal, Swapnamay

doi:10.1103/physrevd.100.125005

Cited by 19 publications

(21 citation statements)

References 110 publications

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“…Finally, we note that other aspects of 1/N expansions in the SYK model were discussed in [54][55][56] but they do not overlap with the present work. This paper is organized as follows: In section 2, we define the SYK model, discuss the moment method and introduce the graphical representations for the calculation of the moments.…”

Section: Introductionmentioning

confidence: 52%

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

García-García

Jia

Verbaarschot

2018

J. High Energ. Phys.

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We analytically evaluate the moments of the spectral density of the q-body Sachdev-Ye-Kitaev (SYK) model, and obtain order 1/N 2 corrections for all moments, where N is the total number of Majorana fermions. To order 1/N , moments are given by those of the weight function of the Q-Hermite polynomials. Representing Wick contractions by rooted chord diagrams, we show that the 1/N 2 correction for each chord diagram is proportional to the number of triangular loops of the corresponding intersection graph, with an extra grading factor when q is odd. Therefore the problem of finding 1/N 2 corrections is mapped to a triangle counting problem. Since the total number of triangles is a purely graph-theoretic property, we can compute them for the q = 1 and q = 2 SYK models, where the exact moments can be obtained analytically using other methods, and therefore we have solved the moment problem for any q to 1/N 2 accuracy. The moments are then used to obtain the spectral density of the SYK model to order 1/N 2 . We also obtain an exact analytical result for all contraction diagrams contributing to the moments, which can be evaluated up to eighth order. This shows that the Q-Hermite approximation is accurate even for small values of N .

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Section: Introductionmentioning

confidence: 52%

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

García-García

Jia

Verbaarschot

2018

J. High Energ. Phys.

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“…This model is very close in the spirit to the colored tensor model (see the book [12]) and it is a particular case of a complex version of the Gross-Rosenhaus SYK generalization proposed in [6]. This particular version of the SYK model has already been studied in [13], [14], [15], [7] and [16].…”

Section: Introductionmentioning

confidence: 79%

Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model

et al. 2019

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We study the effect of non-Gaussian average over the random couplings in a complex version of the celebrated Sachdev-Ye-Kitaev (SYK) model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in N . We then derive the form of the effective action to all orders. An explicit computation of the modification of the variance in the case of a quartic perturbation is performed for both the complex SYK model mentioned above and the SYK generalization proposed in D. Gross and V. Rosenhaus, JHEP 1702 (2017) 093.

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“…In order to compute the amplitudes A(G)| δ0(G)=δ , one must first identify the SYK graphs contributing at order δ 0 (G) = δ. This was done for graphs of order zero [28] and one [4,12]. The procedure was described for higher orders in [4] and further detailed in [26].…”

Section: 3mentioning

confidence: 99%

Combinatorial study of graphs arising from the Sachdev–Ye–Kitaev model

Fusy

Lionni

Tanasă

2020

European Journal of Combinatorics

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We consider the graphs involved in the theoretical physics model known as the colored Sachdev-Ye-Kitaev (SYK) model. We study in detail their combinatorial properties at any order in the so-called 1/N expansion, and we enumerate these graphs asymptotically.Because of the duality between colored graphs involving q + 1 colors and colored triangulations in dimension q, our results apply to the asymptotic enumeration of spaces that generalize unicellular maps -in the sense that they are obtained from a single building block -for which a higherdimensional generalization of the genus is kept fixed.

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Conformality of 1/N corrections in Sachdev-Ye-Kitaev-like models

Cited by 19 publications

References 110 publications

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

Exact moments of the Sachdev-Ye-Kitaev model up to order 1/N2

Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model

Combinatorial study of graphs arising from the Sachdev–Ye–Kitaev model

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