# A note on the SYK model with complex fermions

## TL;DR

This paper investigates a complex fermion version of the SYK model, calculating four-point functions and analyzing chaos, revealing that the $U(1)$ charge mode does not exhibit chaos.

## Contribution

It applies the shadow formalism to the complex fermion SYK model and computes the retarded kernel, providing new insights into operator dimensions and chaos behavior.

## Key findings

- Four-point functions computed in leading order in 1/N
- Retarded kernel analyzed, showing zero Lyapunov exponent for $U(1)$ charge mode
- Operator dimensions identified in the complex fermion SYK model

## Abstract

We consider a version of the Sachdev-Ye-Kitaev model with complex fermions. We apply the shadow formalism to find four-point functions in the leading order in $1/N$ and dimensions of operators present in the theory. We also compute the retarded kernel and show that the Lyapunov exponent for the mode corresponding to the $U(1)$ charge is zero.