Contents Online

# Annals of Mathematical Sciences and Applications

## Volume 2 (2017)

### Number 1

### Higher-dimensional supertranslations and Weinberg’s soft graviton theorem

Pages: 69 – 94

DOI: http://dx.doi.org/10.4310/AMSA.2017.v2.n1.a2

#### Authors

#### Abstract

Asymptotic symmetries of theories with gravity in $d = 2m + 2$ spacetime dimensions are reconsidered for $m \gt 1$ 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 $\mathcal{S}$-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 $d \gt 4$. 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.