A note on the SYK model with complex fermions
Ksenia Bulycheva
TL;DR
This work analyzes a complex fermion version of the SYK model with a global $U(1)$ symmetry by computing leading-$1/N$ four-point functions using the shadow formalism and extracting operator dimensions from the conformal kernel. It also evaluates the retarded kernel to study real-time dynamics, finding a conserved $U(1)$ charge mode with $h=0$ and its $h=1$ partner, and showing a pole at $h=1$ in the four-point function that is removed by inverse coupling corrections in the large-$q$ limit. Crucially, the charge mode is an eigenfunction of the retarded kernel but has a zero Lyapunov exponent, indicating non-chaotic behavior for this sector. The results clarify how complex SYK shares the near-conformal structure of the original model while distinguishing the chaotic properties of the charge sector, with potential implications for holography and strange metal phenomenology.
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.