We analyze in this paper the large N limit of the Schwinger-Dyson equations in tensor quantum field theory, which are derived with the help of Ward-Takahashi identities. In order to have a well-defined large N limit, appropriate scalings in powers of N for the various terms present in the action are explicitly found. A perturbative check of our results is done, up to second order in the coupling constant.
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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