Higher-Dimensional Fermionic SYK Model in IR Region

Abstract

We study the 2D fermionic SYK model with Majorana fermions, featuring a quartic kinetic term and a $2q$-body interaction with Gaussian disorder. By minimizing the effective action or solving the SD equation for $q=1$, we determine that the appropriate ansatz involves zero spins. Our computation of the Lyapunov exponent shows violations of chaos and unitarity bounds. The gravitational dual corresponds to AdS${}_3$ Einstein gravity with a finite radial cut-off, even if we lose the non-zero spins. We also extend the SYK model to higher dimensions while maintaining a similar SD equation in the IR.

20 pages, 3 figures, minor changes, reference added