Asymptotic symmetries and charges at null infinity: from low to high spins

TL;DR

This paper reviews the connection between asymptotic symmetries and Weinberg's soft theorem across different spins, highlighting the existence of higher-spin supertranslations in four dimensions and the challenges in extending these symmetries to higher dimensions.

Contribution

It identifies higher-spin supertranslations and superrotations in four dimensions and discusses their relation to Weinberg's theorem, noting the absence of such symmetries in higher dimensions.

Findings

Higher-spin supertranslations are identified in four dimensions.

No infinite-dimensional asymptotic symmetry enhancement in dimensions greater than four.

The procedure is consistent across dimensions but does not produce new symmetries beyond four.

Abstract

Weinberg's celebrated factorisation theorem holds for soft quanta of arbitrary integer spin. The same result, for spin one and two, has been rederived assuming that the infinite-dimensional asymptotic symmetry group of Maxwell's equations and of asymptotically flat spaces leave the S-matrix invariant. For higher spins, on the other hand, no such infinite-dimensional asymptotic symmetries were known and, correspondingly, no a priori derivation of Weinberg's theorem could be conjectured. In this contribution we review the identification of higher-spin supertranslations and superrotations in $D=4$ as well as their connection to Weinberg's result. While the procedure we follow can be shown to be consistent in any $D$, no infinite-dimensional enhancement of the asymptotic symmetry group emerges from it in $D>4$, thus leaving a number of questions unanswered.