Asymptotic charges from soft scalars in even dimensions

TL;DR

This work investigates asymptotic charges associated to a spin-zero analogue of Weinberg's soft theorems in even spacetime dimensions, focusing on tree-level massless $\varphi^3$ theory in $D=2m+2$ and its extension to massive fields. The authors define a charge $Q(\hat{q})$ at null infinity and relate it to an angular density $\sigma(\hat{x})$ defined from the asymptotic field data, showing a precise map $\sigma(\hat{x}) = \mathbb{K} \, Q(\hat{x})$ with an invertible operator $\mathbb{K}$ on the sphere; the inverse is given by a shadow transform. They extend the analysis to massive fields, establish matching between soft and hard parts across null and time-like infinities, and formulate smeared charges $\sigma[\lambda]$ as total-derivative spacetime currents $j^a=\partial_b k^{ab}$ with a constructed $\Lambda$ from the smearing function $\lambda$. The results provide a concrete field-theoretic interpretation of spin-zero asymptotic charges in higher dimensions and lay groundwork for future work to uncover the underlying symmetry principles, potentially connecting to bi-adjoint or double-copy structures.

Abstract

We study asymptotic charges associated to a spin-zero analogue of Weinberg's soft photon and graviton theorems in even dimensions. Simple spacetime expressions for the charges are given, but unlike gravity or electrodynamics, the symmetry interpretation for the charges remains elusive. This work is a higher dimensional extension of the four dimensional case studied in arXiv:1703.07885 .