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

TL;DR

This paper challenges the idea that different orders of soft theorems are governed by distinct asymptotic symmetries, showing instead that the sub-leading soft photon theorem arises from the same symmetry as the leading one.

Contribution

It demonstrates that the sub-leading soft photon theorem can be derived from the same residual gauge symmetry responsible for the leading theorem.

Findings

Sub-leading soft factor originates from the same symmetry as the leading one.

Expanding the charge in inverse powers of radial coordinate yields soft factors.

Challenges the notion of different symmetries controlling different soft theorem orders.

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.