# Uplifting AdS3/CFT2 to Flat Space Holography

## TL;DR

This paper explores the connection between 4D flat space quantum gravity and AdS3/CFT2 holography, revealing how superrotations act as conformal transformations and identifying a new conformally soft mode in 4D gravity.

## Contribution

It demonstrates that 4D superrotations correspond to conformal transformations on hyperbolic slices and introduces a second conformally soft mode in 4D quantum gravity.

## Key findings

- Superrotations act as conformal transformations on hyperbolic slices.
- The 4D celestial stress tensor is an uplift of the AdS3 holographic stress tensor.
- Discovery of a second conformally soft mode in 4D gravity.

## Abstract

Four-dimensional (4D) flat Minkowski space admits a foliation by hyperbolic slices. Euclidean AdS3 slices fill the past and future lightcones of the origin, while dS3 slices fill the region outside the lightcone. The resulting link between 4D asymptotically flat quantum gravity and AdS3/CFT2 is explored in this paper. The 4D superrotations in the extended BMS4 group are found to act as the familiar conformal transformations on the 3D hyperbolic slices, mapping each slice to itself. The associated 4D superrotation charge is constructed in the covariant phase space formalism. The soft part gives the 2D stress tensor, which acts on the celestial sphere at the boundary of the hyperbolic slices, and is shown to be an uplift to 4D of the familiar 3D holographic AdS3 stress tensor. Finally, we find that 4D quantum gravity contains an unexpected second, conformally soft, dimension (2, 0) mode that is symplectically paired with the celestial stress tensor.