Soft gravitons in three dimensions

We consider quantum gravity with zero cosmological constant in three dimensions. First, we show that pure quantum gravity can be written as a magnetic Carrollian theory living on null infinity, described by Schwarzian-like degrees of freedom. Next, we couple quantum gravity to massless matter. Transition amplitudes exhibit several features that resemble soft graviton physics in four dimensions, despite the absence of a propagating graviton. As in four dimensions, we find three equivalent results: a soft graviton theorem, an infinite-dimensional BMS asymptotic symmetry, and a gravitational memory effect. We also resolve some extant puzzles concerning the partition function and Hilbert space of pure 3d gravity with zero cosmological constant.