Abstract
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski space. We then identify higher-spin supertranslations and generalised superrotations in any dimension. These symmetries are in one-to-one correspondence with spin-s partially-massless representations on the celestial sphere, with supertranslations corresponding in particular to the representations with maximal depth. We discuss the definition of the corresponding asymptotic charges and we exploit the supertranslational ones in order to prove the link with Weinberg’s soft theorem in even dimensions.
Highlights
As for what concerns the asymptotic structure of asymptotically flat spacetimes
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four
Assuming the asymptotic expansion in retarded Bondi coordinates φus−kik (r, u, x) = r−n Uik(k,n)(u, x), n we investigate the asymptotic structure of the gauge symmetries of the form δφμs = ∇μ μs−1 with gαβ αβμs−3 = 0 (2.3)
Summary
The presence of these overleading field components may be source of subtleties in general, as the definition of superrotation charges to be discussed in section 3 testifies With this proviso, we take the same attitude for any spin: we assume overall falloffs as weak as φ φ us−kik us−k ik = O(r−2) for any s in any D, we identify the u−independent residual symmetries preserving (2.1) and we argue that above the radiation order only pure-gauge configurations survive on shell, while leaving to the section a detailed derivation of these results. In order to connect the Ward identity of higher-spin supertranslations to the soft theorem it is useful once again to make use of a specific form of T (x), Tw (x) = (Dw )is Substituting this relation into the spin-s version of the Ward identity (2.26) yields the s-divergence of Weinberg’s theorem. The reverse implication, on the other hand, namely that Weinberg’s theorem yields the Ward identity (2.26) as well as its spin-s counterpart, is of less relevance in the context of higher spins given that Weinberg’s result implies the vanishing of the soft couplings for s > 2
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