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We consider the tree-level scattering of massless particles in d+2-dimensional asymptotically flat spacetimes. The S-matrix elements are recast as correlation functions of local operators living on a space-like cut of the null momentum cone. The Lorentz group **SO(d+1,1)** is nonlinearly realized as the Euclidean conformal group on the spatial cut. Using the soft-photon and soft-graviton theorems, we construct the **U(1)** current **J_a** and stress-tensor operator **T_{ab}** for the boundary CFT.

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