Soft Photon and Graviton Theorems in Effective Field Theory

TL;DR

This work analyzes soft theorems in 4d local EFTs with massless states, showing that EFT operators can modify soft photon and graviton factors at subleading and subsubleading orders and classifying exactly which operators can do so. A novel on-locus soft-limit via a complex double deformation yields a master equation encoding key consistency conditions, including charge conservation, the equivalence principle, SUSY Ward identities, and Weinberg-Witten constraints. Crucially, subleading soft graviton modifications are forbidden by locality/unitarity, while a universal subsubleading correction arises from a small set of dimensionful operators. The results connect soft-theorem universality to fundamental principles and shed light on how EFT corrections interact with asymptotic symmetries and supergravity.

Abstract

Extensions of the photon and graviton soft theorems are derived in 4d local effective field theories with massless particles of arbitrary spin. We prove that effective operators can result in new terms in the soft theorems at subleading order for photons and subsubleading order for gravitons. The new soft terms are unique and we provide a complete classification of all local operators responsible for such modifications. We show that no local operators can modify the subleading soft graviton theorem. The soft limits are taken in a manifestly on-locus manner using a complex double deformation of the external momenta. In addition to the new soft theorems, the resulting master formula yields consistency conditions such as the conservation of electric charge, the Einstein equivalence principle, supergravity Ward identities, and the Weinberg-Witten theorem.