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

## TL;DR

This paper investigates how non-Gaussian averaging over couplings affects the complex SYK model, revealing modifications to the variance and deriving the effective action to all orders.

## Contribution

It introduces a method to incorporate non-Gaussian disorder averaging into the SYK model and computes the resulting variance modifications explicitly.

## Key findings

- Non-Gaussian averaging modifies the variance of couplings at leading order.
- Derived the form of the effective action to all orders.
- Explicitly computed variance modifications for quartic perturbations.

## 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.