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.
Categories: hep-th gr-qc