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

Abstract

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.

arXiv comment21 pages, 7 figures, minor changes

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• Remarks on a melonic field theory with cubic interaction
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• Towards quantum simulation of Sachdev-Ye-Kitaev model
• Double scaling limit for the $O(N{)}^3$-invariant tensor model
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications