Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem

TL;DR

The paper resolves a tension in higher-dimensional gravity: previous work suggested no supertranslations beyond four dimensions due to strong boundary conditions, while Weinberg's soft graviton theorem persists in any even dimension. By relaxing the asymptotic boundary conditions to permit zero-energy large diffeomorphisms, Kapec–Lysov–Pasterski–Strominger show the BMS group, including supertranslations, remains the asymptotic symmetry in all even dimensions. They derive a Ward identity from Weinberg's soft theorem and identify corresponding charges that decompose into hard (matter) and soft (gravitational) parts, with the soft part generating supertranslations on the radiative data. The results establish a direct link between infrared structure and asymptotic symmetries in arbitrary even dimensions, extending the soft theorem–Ward identity correspondence beyond four dimensions and suggesting further exploration of nonlinear effects and odd 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.