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We use the subleading soft-graviton theorem to construct an operator Tₙₙ 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.
Kapec et al. (Fri,) studied this question.
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