  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.
