Towards the holographic dual of N = 2 $$ \mathcal{N}=2 $$ SYK

Abstract

Abstract The gravitational part of the holographic dual to the SYK model has been conjectured to be Jackiw-Teitelboim (JT) gravity. In this paper we construct an AdS2 background in N = 2 , 2 $$ \mathcal{N}=\left(2,\ 2\right) $$ JT gravity and show that the gravitational dynamics are — as in the N = 0 $$ \mathcal{N}=0 $$ and N = 1 $$ \mathcal{N}=1 $$ cases — fully captured by the extrinsic curvature as an effective boundary action. This boundary term is given by the super-Schwarzian of the N = 2 $$ \mathcal{N}=2 $$ SYK model, thereby providing further evidence of the JT/SYK duality. The chirality of this SYK model is reproduced by the inherent chirality of axial N = 2 , 2 $$ \mathcal{N}=\left(2,\ 2\right) $$ supergravity.

Keywords

• 2D Gravity
• AdS-CFT Correspondence
• Extended Supersymmetry