A 2D Stress Tensor for 4D Gravity

TL;DR

Kapec et al. show that 4D gravity amplitudes in asymptotically flat spacetime can be recast as 2D celestial CFT correlators on the sphere at null infinity. By exploiting the subleading soft-graviton theorem, they construct a holomorphic 2D stress tensor T_{zz} whose insertions in tree-level amplitudes satisfy the Virasoro Ward identities, indicating a Virasoro representation behind gravity scattering. They define the relevant News zero-mode and its associated nonlocal construct N^{(1)} and demonstrate how T_{zz} generates local conformal transformations on the celestial sphere via contour charges. The work clarifies the correspondence between 4D gravitational dynamics and 2D conformal symmetries, while noting limitations such as the massless restriction, potential central terms with multiple soft insertions, and unknown unitary properties of the resulting representations.

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.