On asymptotic symmetries in higher dimensions for any spin

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.

Charge algebra for non-abelian large gauge symmetries at O(r)

“…Theories with massless fields in asymptotically flat spacetimes exhibit a rich structure at null infinity [1][2][3] that is reflected in their asymptotic symmetry groups. Well known examples are large gauge symmetries in Yang-Mills (YM) theory [6], Bondi-Metzner-Sachs (BMS) diffeomorphisms in gravity [4,5], and their higher spin versions [7,8].…”

General null asymptotics and superrotation-compatible configuration spaces in d ≥ 4

“…The arguments imply that the round sphere boundary metric γ AB (x) should be extended to a generic h (0)AB (x). The linearisation of the relevant equations of [64] gives those of [70], as can be checked in a covariant way in this paper (the linear version of (3.8) with β (0) = 0). In the next subsections we explicitly show that such metrics must not satisfy the Einstein condition, and hence in the linearised approach of [70], the perturbation of γ is such that γ + is not Einstein.…”

“…We have not discussed, as in previous analysis [60,70,95], the gauge character of h (1)AB and the other overleading terms before the radiative order. As we can see from [60,70,95], the proof that h (1)AB is pure gauge strictly depends on the assumption that the boundary metric h (0)AB is the time-independent round sphere metric and on the properties of the Laplacian associated to this metric. We are thus agnostic about this result for more general Einstein or non-Einstein, time-independent or time-dependent metrics.…”

“…Thus no consistent proposal of superrotation charge can be made on the KLPS configuration space. With a different take, a u-dependence for h (1)AB is obtained in the later linear analysis of [70] around Minkowski spacetime. Here, the time dependence of h (1) is due to timeindependent deformations of the leading round sphere metric γ AB at the linear level.…”

“…As we have reviewed in subsection 2.2, while supertranslations can be defined at the linear level in higher dimensions, superrotations cannot be defined on the same configuration space. In section 3.2 we have discussed the boundary conditions that allow to bypass the issues experienced by previous literature (sections 3.1 and 3.2.1) and we have recognised the case in claim C.1 as corresponding to the case discussed only in five spacetime dimension in [64] and at a linear level in [70].…”