Asymptotic Symmetries and Subleading Soft Photon Theorem in Effective Field Theories

TL;DR

The paper shows that the subleading soft photon theorem in tree-level EFTs containing photons is a Ward identity for the ${\mathcal{S}}$-matrix associated to divergent large $U(1)$ gauge transformations on null infinity. Higher-derivative interactions introduce non-universal corrections to the subleading theorem, but these corrections appear through controlled, operator-specific terms and share the same kinematic structure, ensuring a consistent relation between soft theorems and asymptotic charges. The authors construct corrected subleading charges, both electric and magnetic, and demonstrate the equivalence between Ward identities and the subleading soft theorem, including a detailed treatment of mode expansions and the celestial-sphere representation. These results strengthen the view that soft theorems encode infinite-dimensional asymptotic symmetries and hint at holographic interpretations on the celestial sphere, with potential extensions to sub-subleading theorems in gravity.

Abstract

In [1,2] it was shown that the subleading soft photon theorem in tree level amplitudes in massless QED is equivalent to a new class of symmetries of the theory parameterized by a vector field on the celestial sphere. In this paper, we extend these results to the subleading soft photon theorem in any Effective Field Theory containing photons and an arbitrary spectrum of massless particles. We show that the charges associated to the above class of symmetries are sensitive to certain three point functions of the theory and are corrected by irrelevant operators of specific dimensions. Our analysis shows that the subleading soft photon theorem in any tree level scattering amplitude is a statement about asymptotic symmetries of the ${\cal S}$-matrix.