Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem

TL;DR

This paper extends the understanding of asymptotic symmetries in higher-dimensional gravity, linking supertranslations to soft gravitons and reinterpreting Weinberg's theorem as a Ward identity in even dimensions.

Contribution

It identifies higher-dimensional supertranslations as asymptotic symmetries and connects them to soft gravitons, providing an alternative derivation and challenging previous boundary condition assumptions.

Findings

Supertranslations exist in all even dimensions greater than four.

Soft gravitons are Goldstone bosons of spontaneously broken supertranslation symmetry.

Weinberg's soft graviton theorem is expressed as a Ward identity in higher dimensions.

Abstract

Asymptotic symmetries of theories with gravity in d=2m+2 spacetime dimensions are reconsidered for m>1 in light of recent results concerning d=4 BMS symmetries. Weinberg's soft graviton theorem in 2m+2 dimensions is re-expressed as a Ward identity for the gravitational S-matrix. The corresponding asymptotic symmetries are identified with 2m+2-dimensional supertranslations. An alternate derivation of these asymptotic symmetries as diffeomorphisms which preserve finite-energy boundary conditions at null infinity and act non-trivially on physical data is given. Our results differ from those of previous analyses whose stronger boundary conditions precluded supertranslations for d>4. We find for all even d that supertranslation symmetry is spontaneously broken in the conventional vacuum and identify soft gravitons as the corresponding Goldstone bosons.