Higher-dimensional supertranslations and Weinberg’s soft graviton theorem

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.

Burg-Metzner-Sachs symmetry, string theory, and soft theorems

“…This suggests the use of more lenient boundary conditions that allow for BMS type symmetries in d > 4. Such a solution has been suggested in [37] and this is what we advocate in this paper in the context of string theory. Interestingly, it seems that string theory even prefers boundary conditions that allow for the discussed symmetry enhancement in any dimension.…”

On higher-spin supertranslations and superrotations

“…6 Alternative boundary conditions for gravity -designed to keep supertranslations also when the dimension of space-time is larger than four -have been proposed in [37]. A similar option may be foreseen for higher spins too; we postpone an analysis of this issue to future work.…”

“…The previous discussion formally applies also to odd space-time dimensions, which the analysis of [26,36] does not encompass, while in the special n = 2 case the first relation in (6.5) is substituted by the weaker condition (4.18), involving a u-derivative of the same tensors. Analogy with the gravitational falloffs and consistency with the linearised field equations are our main motivations for imposing the boundary conditions (6.2)-(6.5), where one could also adopt a conservative viewpoint and bound the value of n to be even in analogy with [26,36,37]. 8 We are now going to identify the residual gauge transformations leaving them invariant.…”

Flat holography: aspects of the dual field theory

“…This means that the theorem would lead to an infinite number of Ward identities which will naturally lead to the expectation of an infinite dimensional supertranslation sub-group. This has been recently discussed in [69]. 6 With this in mind, we explore the possible infinite lift of the BMS group in higher dimensions.…”