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

TL;DR

This paper develops a $d$-dimensional stress tensor framework for Minkowski gravity in $(d+2)$ dimensions, connecting scattering amplitudes to conformal correlators and revealing soft theorems as Ward identities.

Contribution

It introduces a novel $d$-dimensional stress tensor formalism for Minkowski gravity, linking scattering amplitudes to conformal field theory structures on a null momentum cut.

Findings

Soft operators correspond to conserved currents and stress tensors.

Scattering amplitudes are recast as conformal correlators.

Soft theorems are shown to be Ward identities.

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.