Asymptotic Symmetries and Weinberg's Soft Photon Theorem in Mink$_{d+2}$

TL;DR

This work shows that Weinberg's leading soft photon theorem is the Ward identity of an infinite-dimensional large U(1) gauge symmetry acting on the null boundaries ${\mathscr I}^{\pm}$ in $(d+2)$-dimensional Minkowski space, extending the soft-theorem–asymptotic-symmetry link to all dimensions, including odd ones. The authors develop a detailed asymptotic analysis of $U(1)$ gauge theory in $d+2$ dimensions, define radiative and Coulombic contributions, and construct soft and hard charges via antipodal matching on ${\mathscr I}^{\pm}$. They then connect these charges to the soft-photon insertion in the S-matrix through Ward identities, and show that the soft charge generates large gauge transformations on the celestial boundaries within the covariant phase-space framework. The results unify previous dimension-specific findings, clarify the role of memory and celestial-holography aspects, and establish a robust framework for asymptotic symmetries in higher (including odd) dimensions.

Abstract

We show that Weinberg's leading soft photon theorem in massless abelian gauge theories implies the existence of an infinite-dimensional large gauge symmetry which acts non-trivially on the null boundaries ${\mathscr I}^\pm$ of $(d+2)$-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function $\varepsilon(x)$ of the $d$-dimensional celestial sphere living at ${\mathscr I}^\pm$. This extends the previously established equivalence between Weinberg's leading soft theorem and asymptotic symmetries from four and higher even dimensions to \emph{all} higher dimensions.