Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities

TL;DR

This paper demonstrates that soft theorems for photons, gluons, and gravitons can be derived as Ward-Takahashi identities of large gauge transformations, revealing infinitely many new identities constraining higher-order soft behaviors.

Contribution

It introduces an infinite set of soft theorems as Ward-Takahashi identities, extending the understanding of gauge and gravity scattering amplitudes.

Findings

Identified infinitely many new soft theorems

Connected soft theorems to large gauge transformations

Provided diagrammatic representations of the theorems

Abstract

We show that the soft photon, gluon and graviton theorems can be understood as the Ward-Takahashi identities of large gauge transformation, i.e., diffeomorphism that does not fall off at spatial infinity. We found infinitely many new identities which constrain the higher order soft behavior of the gauge bosons and gravitons in scattering amplitudes of gauge and gravity theories. Diagrammatic representations of these soft theorems are presented.