Mapping SYK to the Sky

TL;DR

This paper proposes that a 2D generalization of the SYK model can serve as a toy model capturing the symmetries and soft dynamics of 4D gravitational theories in asymptotically flat spacetime, aiding holographic duality studies.

Contribution

It introduces a 2D SYK-based model that reflects key features of celestial holography, including symmetries and chaotic behavior, using the Penrose twistor transform.

Findings

2D SYK model exhibits celestial symmetries like $w_{1+ ext{infinity}}$

Model captures chaotic and conformal dynamics of 4D gravity

Holographic map employs Penrose twistor transform

Abstract

The infrared behavior of gravity in 4D asymptotically flat spacetime exhibits a rich set of symmetries. This has led to a proposed holographic duality between the gravitational $\mathcal{S}$-matrix and a dual field theory living on the celestial sphere. Most of our current understanding of the dictionary relies on knowledge of the 4D bulk. As such, identifying intrinsic 2D models that capture the correct symmetries and soft dynamics of 4D gravity is an active area of interest. Here we propose that a 2D generalization of SYK provides an instructive toy model for the soft limit of the gravitational sector in 4D asymptotically flat spacetime. We find that the symmetries and soft dynamics of the 2D SYK model capture the salient features of the celestial theory: exhibiting chaotic dynamics, conformal invariance, and a $w_{1+\infty}$ symmetry. The holographic map from 2D SYK operators to the 4D bulk employs the Penrose twistor transform.