A d-dimensional stress tensor for Minkd+2 gravity

We consider the tree-level scattering of massless particles in (d+2)-dimensional asymptotically flat spacetimes. The S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{S} $$\end{document}-matrix elements are recast as correlation functions of local operators living on a space-like cut ℳd of the null momentum cone. The Lorentz group SO(d + 1, 1) is nonlinearly realized as the Euclidean conformal group on ℳd. 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 Ja, and the subleading soft-graviton operator is the shadow transform of a conserved spin-two symmetric traceless primary operator Tab. The universal form of the soft-limits ensures that Ja and Tab obey the Ward identities expected of a conserved current and energy momentum tensor in a Euclidean CFTd, respectively.