Remarks on Asymptotic Symmetries and the Sub-leading Soft Photon Theorem

Abstract: A deep connection has been recently established between soft theorems and symmetries at null infinity in gravity and gauge theories, recasting the former as Ward identities of the latter. In particular, different orders (in the frequency of the soft particle) in the soft theorems are believed to be controlled by different asymptotic symmetries. In this paper we argue that this needs not be the case by focusing on the soft photon theorem. We argue that the sub-leading soft factor follows from the same symmetry responsible for the leading one, namely certain residual (large) gauge transformations of the gauge theory. In particular, expanding the associated charge in inverse powers of the radial coordinate, the (sub-)leading charge yields the (sub-)leading soft factor.