Finite actions and asymptotic charges at null infinity for any spin

TL;DR

The paper develops a local, spin-agnostic boundary renormalization framework for free massless fields at null infinity in D>4, under boundary conditions that admit higher-spin supertranslations. By combining a Bondi-like gauge with a specifically crafted boundary term, it cancels the leading divergences of the on-shell action while preserving the variational principle, and it clarifies how corner terms relate to renormalized surface charges. The approach yields finite expressions for the renormalized action and supertranslation charges, generalizing Ashtekar–Streubel-like structures to arbitrary spin, and discusses the interplay between gauge ambiguities, corner contributions, and possible covariant reformulations. The work also outlines extensions to covariance, non-linear theories, and potential connections to flat-space holography and Carrollian boundary structures.

Abstract

We identify boundary terms renormalizing the free on-shell actions for massless fields of arbitrary spin, including electromagnetism and linearized gravity, with boundary conditions allowing for supertranslation-like asymptotic symmetries. Our focus is on null infinity, in any spacetime dimensions. We also comment on the renormalization of the corresponding asymptotic charges.