Subleading soft photons and large gauge transformations

TL;DR

This work reframes Low's subleading soft photon theorem as Ward identities of a new class of large U(1) gauge transformations in massless QED. It shows that both electric- and magnetic-type charges associated with O(1) and O(r) asymptotic gauge parameters encode the leading and subleading soft theorems, with a finite formulation obtained by projecting out soft contributions. By decomposing the O(r) parameters into gradient and curl components, the subleading relation is demonstrated to arise from a sum of electric and magnetic charges, paralleling the leading-soft story. The authors argue that higher-than-linear divergences in the gauge parameter do not yield additional symmetries, and they anticipate a gravitational analog for sub-subleading behavior. Overall, the framework deepens the connection between asymptotic symmetries and soft theorems and sets the stage for quantum and loop-order extensions.

Abstract

Lysov, Pasterski and Strominger have shown how Low's subleading soft photon theorem can be understood as Ward identities of new symmetries of massless QED. In this paper we offer a different perspective and show that there exists a class of large $U(1)$ gauge transformations such that (i) the associated (electric and magnetic) charges can be computed from first principles (ii) their Ward identities are equivalent to Low's theorem. Our framework paves the way to analyze the sub-subleading theorem in gravity in terms of Ward identities associated to large diffeomorphisms.