Holographic dual to charged SYK from 3D Gravity and Chern-Simons

Understand

In this paper, we obtain a bulk dual to SYK model, including SYK model with $U(1)$ charge, by Kaluza-Klein (KK) reduction from three dimensions.

• We show that KK reduction of the 3D Einstein action plus its boundary term gives the Jackiw-Teitelboim (JT) model in 2D with the appropriate 1D boundary term.
• The size of the KK radius gets identified with the value of the dilaton in the resulting near-AdS$_2$ geometry.
• In presence of U(1) charge, the 3D model additionally includes a $U(1)$ Chern-Simons (CS) action.