3D Stress Tensor for Gravity in 4D Flat Spacetime

TL;DR

This paper demonstrates that the 3d Carrollian stress tensor at null infinity encodes soft graviton theorems and connects to celestial holography, providing insights into flat spacetime holographic dualities.

Contribution

It shows how the 3d Carrollian stress tensor encodes soft graviton theorems and relates to the celestial stress tensor, bridging flat space holography and celestial CFTs.

Findings

The 3d Carrollian stress tensor encodes leading and subleading soft graviton theorems.

The 3d Carrollian stress tensor relates to the 2d celestial stress tensor.

The approach connects flat space holography with celestial CFTs.

Abstract

Three dimensional (3d) Carrollian CFTs are potential co-dimension one holographic duals of 4d asymptotically flat spacetimes that live on the whole of the null boundary. In this paper, we show that the local stress tensor of the 3d Carrollian conformal theory (without any additional sources) constructed in terms of the geometric structure at asymptotic null infinity naturally encodes both the leading and subleading soft graviton theorems. We relate the 3d Carroll stress tensor to the 2d Celestial one and show how the 3d version naturally localises the non-local 2d Celestial stress tensor. We also comment on the relation with stress tensors in relativistic 3d CFTs and connections to the flat limit of AdS/CFT.