Soft Photon and Graviton Theorems in Effective Field Theory

TL;DR

This paper extends soft photon and graviton theorems within 4d effective field theories, identifying new terms at subleading orders and classifying operators responsible, while confirming some theorems remain unmodified.

Contribution

It provides a complete classification of local operators affecting soft theorems and proves the invariance of the subleading soft graviton theorem in effective field theories.

Findings

New soft photon terms at subleading order

No local operators modify the subleading soft graviton theorem

Master formula yields various consistency conditions

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.