Asymptotic Charges at Null Infinity in Any Dimension

TL;DR

This work develops a uniform framework for large-gauge asymptotic symmetries and finite charges of massless bosons across arbitrary spacetime dimensions, extending beyond spin two to spin three and arbitrary spin $s$. By implementing Bondi-like falloffs and solving the equations of motion in Yang–Mills, linearised gravity, and higher-spin Fronsdal formalisms, it identifies radiation and Coulomb branches and derives finite, integrable charges up to null infinity. A key outcome is the dimensional dependence: for $D>4$ the asymptotic symmetry algebra is finite (global color/Poincaré), while in $D=4$ and $D=3$ infinite-dimensional enhancements (Kač–Moody and BMS-like structures) appear, with charges potentially carrying retarded-time dependence in 4D due to radiation data. The paper also provides explicit spin-3 and general-spin boundary-condition recipes and expresses charges via on-shell closed two-forms in Bondi gauge, linking the infrared structure to soft-theorem Ward identities and suggesting paths to a non-perturbative higher-spin asymptotic symmetry algebra.

Abstract

We analyse the conservation laws associated with large gauge transformations of massless fields in Minkowski space. Our aim is to highlight the interplay between boundary conditions and finiteness of the asymptotically conserved charges in any space-time dimension, both even and odd, greater than or equal to three. After discussing non-linear Yang-Mills theory and revisiting linearised gravity, our investigation extends to cover the infrared behaviour of bosonic massless quanta of any spin.