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

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 ${\mathcal{I}}^{\pm }$ of $(d+2)$-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function $\epsilon (x)$ of the $d$-dimensional celestial sphere living at ${\mathcal{I}}^{\pm }$. 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.

Comments: 30 pages; v2: Added reference and minor clarification comments, fixed minor typos, version to appear in JHEP; v3: Corrected minor typo in equation