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

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.