Higher-Dimensional Fermionic SYK Model in IR Region

TL;DR

This paper investigates a 2D fermionic SYK model with Majorana fermions, analyzing its chaotic behavior, gravitational dual, and extending the model to higher dimensions, revealing violations of chaos bounds and connections to AdS$_3$ gravity.

Contribution

It introduces a higher-dimensional fermionic SYK model with a quartic kinetic term and explores its IR behavior, chaos properties, and gravitational duals, extending previous SYK models.

Findings

Violations of chaos and unitarity bounds in the model

Correspondence with AdS$_3$ Einstein gravity with a finite radial cut-off

Extension of the SYK model to higher dimensions with similar IR behavior

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.