  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.
