A 2D Stress Tensor for 4D Gravity

TL;DR

This paper constructs a 2D stress tensor operator in 4D gravity using soft-graviton theorems, revealing a conformal structure on the celestial sphere at null infinity.

Contribution

It introduces a new operator $T_{zz}$ satisfying Virasoro-Ward identities, linking 4D quantum gravity to 2D conformal field theory structures.

Findings

Establishes a Virasoro symmetry in 4D gravity amplitudes

Defines a 2D stress tensor operator from 4D scattering data

Connects celestial sphere symmetries to 2D CFT concepts

Abstract

We use the subleading soft-graviton theorem to construct an operator $T_{zz}$ whose insertion in the four-dimensional tree-level quantum gravity $\mathcal{S}$-matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT$_2$). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT$_2$, with the Lorentz group acting as the unbroken $SL(2,\mathbb{C})$ subgroup.