A $d$-Dimensional Stress Tensor for Mink${}_{d+2}$ Gravity

Abstract

We consider the tree-level scattering of massless particles in $(d+2)$-dimensional asymptotically flat spacetimes. The $\mathcal{S}$-matrix elements are recast as correlation functions of local operators living on a space-like cut ${\mathcal{M}}_d$ of the null momentum cone. The Lorentz group $SO(d+1,1)$ is nonlinearly realized as the Euclidean conformal group on ${\mathcal{M}}_d$. Operators of non-trivial spin arise from massless particles transforming in non-trivial representations of the little group $SO(d)$, and distinguished operators arise from the soft-insertions of gauge bosons and gravitons. The leading soft-photon operator is the shadow transform of a conserved spin-one primary operator $J_a$, and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator $T_{ab}$. The universal form of the soft-limits ensures that $J_a$ and $T_{ab}$ obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFT${}_d$, respectively.

19 pages. v2: Updated acknowledgements and fixed typos

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