Three Dimensional View of the SYK/AdS Duality

TL;DR

The work casts the SYK bulk dual as a three-dimensional theory: a BF-bound scalar propagating on $AdS_2\times (S^1)/Z_2$ with a central delta potential, whose Kaluza-Klein tower reproduces the SYK bi-local spectrum at strong coupling. By tuning the interval size and delta strength, the authors show exact agreement with the strong-coupling poles and demonstrate that the leading $1/J$ corrections align with known SYK results, supporting a 3D bulk interpretation. The analysis leverages a KK decomposition and a linearized gravity background (JT-like dilaton) to connect the AdS$_2$ bulk with the SYK bi-local field, providing a compact re-packaging of the infinite tower of SYK states. This 3D viewpoint opens a pathway to understand higher-dimensional holographic duals of SYK-like models, though nonlinear dynamics and higher-point functions remain to be explored.

Abstract

We show that the spectrum of the SYK model can be interpreted as that of a 3D scalar coupled to gravity. The scalar has a mass which is at the Breitenholer-Freedman bound of AdS$_2$, and subject to a delta function potential at the center of the interval along the third direction. This, through Kaluza-Klein procedure on AdS$_2 \times (S^1)/Z_2$, generates the spectrum reproducing the bi-local propagator at strong coupling. Furthermore, the leading $1/J$ correction calculated in this picture reproduces the known correction to the poles of the SYK propagator, providing credence to a conjecture that the bulk dual of this model can be interpreted as a three dimensional theory.