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 S matrix obeys the Virasoro-Ward identities of the energy momentum tensor of a two-dimensional conformal field theory (CFT2). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT2, with the Lorentz group acting as the unbroken SL(2, C) subgroup.