A 2D Stress Tensor for 4D Gravity

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.

12 pages. v2: updated acknowledgements

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