Ward identity for loop level soft photon theorem for massless QED coupled to gravity

TL;DR

This paper demonstrates the equivalence between the loop-level subleading soft photon theorem and an asymptotic conservation law in massless QED coupled with gravity, highlighting the role of long-range forces in four dimensions.

Contribution

It extends the soft photon theorem and asymptotic charge correspondence to include gravitational effects at loop level in massless QED.

Findings

Soft photon theorem at loop level is equivalent to an asymptotic conservation law.

Long-range gravitational forces contribute to the dressing of soft photons.

Asymptotic charges are related to field dressing due to long-range forces.

Abstract

Strominger and his collaborators pioneered the study of equivalence between soft theorems and asymptotic conservation laws. We study this equivalence in the context of loop level subleading soft photon theorem for massless scalar QED in presence of dynamical gravity. Motivated by Campiglia and Laddha \cite{1903.09133}, we show that the Sahoo-Sen soft photon theorem \cite{1808.03288} for loop amplitudes is equivalent to an asymptotic conservation law. This asymptotic charge is directly related to the dressing of fields due to long range forces exclusively present in four spacetime dimensions. In presence of gravity, the new feature is that soft photons also acquire a dressing due to long range gravitational force and this dressing contributes to the asymptotic charge.