Asymptotic symmetries and subleading soft graviton theorem in higher dimensions

TL;DR

The paper extends the established connection between soft graviton theorems and asymptotic symmetries to higher even dimensions by showing that the subleading soft graviton theorem can be formulated as a Ward identity whose charges realize the group $Diff(S^{2m})$ under appropriately weakened falloff conditions. Through explicit analysis in six dimensions and a generalization to arbitrary even dimensions, the authors derive soft and hard charges and demonstrate how the proposed commutation relations lead to Diff$(S^{2m})$-generated transformations in gravitational scattering at tree level. They discuss divergences in the charge construction and propose renormalization as a necessary step for a fully finite realization, while outlining broader implications for the symmetry structure of gravity in higher dimensions. The work thus reinforces the triangle link between asymptotic symmetries, soft theorems, and memory effects in a dimensionally extended setting and motivates further investigation into non-linear, loop, and odd-dimensional cases.

Abstract

We investigate the relation between the subleading soft graviton theorem and asymptotic symmetries in gravity in even dimensions $d=2+2m$ higher than four. After rewriting the subleading soft graviton theorem as a Ward identity, we argue that the charges of such identity generate Diff$(S^{2m})$. In order to show that, we propose suitable commutation relation among certain components of the metric fields. As a result, all Diff$(S^{2m})$ transformations are symmetries of gravitational scattering.

Figures (1)

• Figure 1: Penrose diagram of Minkowski space. Past and future null infinities are labelled by $\mathcal{I}^{\pm}$ and their boundaries by $\mathcal{I}^{\pm}_{\pm}$. Past and future time-like infinities are labelled by $i^{\pm}$ and spatial infinity by $i^0$.