Space-Time in the SYK Model

TL;DR

This paper investigates the emergent space-time structure in the SYK model, proposing non-local transformations to reveal a dual Euclidean AdS space with additional leg-factors possibly linked to extra bulk states.

Contribution

It introduces non-local Radon-type transformations on Green's functions to identify the bulk space-time signature in the SYK model, suggesting a dual Euclidean AdS with extra leg-factors.

Findings

Dual theory exhibits Euclidean AdS signature with leg-factors.

Leg-factors may encode coupling to additional bulk states.

Highlights the importance of non-local transformations in holographic correspondence.

Abstract

We consider the question of identifying the bulk space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of $n$-point Green's functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2d string theory.