Uplifting AdS3/CFT2 to Flat Space Holography

TL;DR

This work uplifts AdS3/CFT2 holography to flat space by foliating Minkowski space with hyperbolic slices and showing 4D superrotations act as 2D conformal transformations on each slice. It builds covariant phase space charges with soft and hard components, tying the soft sector to a celestial stress tensor that mirrors the AdS3 holographic stress tensor and thereby links 4D asymptotically flat gravity to AdS3 insights. Additionally, it reveals a conformally soft (2,0) mode that is symplectically paired with the celestial stress tensor, hinting at new conformally soft symmetries for the celestial S-matrix and enriching the flat-space holographic framework.

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.

Figures (1)

• Figure 1: Penrose diagram of hyperbolic slicing of Minkowski space. The slices correspond to surfaces of constant $\tau$. The slices in the past and future lightcones of the origin have the geometry of $H_3$, and the slices with spacelike separation from the origin have the geometry of dS$_3$.