Soft gravitons in three dimensions

TL;DR

This paper explores quantum gravity in three dimensions, revealing a magnetic Carrollian structure at null infinity, and demonstrates that soft graviton phenomena like theorems, symmetries, and memory effects are present despite the lack of propagating gravitons.

Contribution

It introduces a novel description of 3D quantum gravity as a magnetic Carrollian theory and establishes the presence of soft graviton physics phenomena in this setting.

Findings

Pure 3D quantum gravity can be formulated as a magnetic Carrollian theory.

Soft graviton theorems, BMS symmetries, and memory effects are observed in 3D.

The study resolves puzzles related to the partition function and Hilbert space of 3D gravity.

Abstract

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.