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

TL;DR

This work analyzes how Weinberg's soft theorem for arbitrary integer spin arises from asymptotic symmetries at null infinity, extending known spin-1/2 and spin-2 results to higher spins. In D=4, it identifies an infinite-dimensional set of higher-spin symmetries—spin-s supertranslations and, for s=3, spin-3 superrotations—whose Ward identities reproduce the soft theorem; in D>4 no such enhancement persists, leaving only global symmetries and finite charges. The analysis develops a dimension-agnostic framework for asymptotic charges, applying it to spin-1 Yang-Mills and general spin-s to reveal a radiation/Coulomb split with dimension-dependent behavior of charges and symmetries. These findings clarify the link between soft theorems and asymptotic symmetries and point to future directions, including non-Abelian higher-spin algebras and potential memory effects.

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.