2D Stress Tensor for 4D Gravity

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 (${\mathrm{CFT}}_2$). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the ${\mathrm{CFT}}_2$, with the Lorentz group acting as the unbroken $SL(2,\mathbb{C})$ subgroup.