Factorized soft graviton theorems at loop level

TL;DR

This paper investigates the behavior of graviton scattering amplitudes at loop level, demonstrating that leading and subleading soft graviton theorems are protected from radiative corrections, with corrections appearing only at the sub-subleading order.

Contribution

It shows that soft graviton operators are highly constrained by symmetries and that radiative corrections only affect the sub-subleading order at one-loop, depending on two coefficients.

Findings

Leading and subleading soft graviton theorems are uncorrected at loop level.

Radiative corrections first appear at the sub-subleading order and are one-loop exact.

Corrections depend on two undetermined coefficients reflecting the theory's field content.

Abstract

We analyze the low-energy behavior of scattering amplitudes involving gravitons at loop level in four dimensions. The single-graviton soft limit is controlled by soft operators which have been argued to separate into a factorized piece and a non-factorizing infrared divergent contribution. In this note we show that the soft operators responsible for the factorized contributions are strongly constrained by gauge and Poincare invariance under the assumption of a local structure. We show that the leading and subleading orders in the soft-momentum expansion can not receive radiative corrections. The first radiative correction occurs for the sub-subleading soft graviton operator and is one-loop exact. It depends on only two undetermined coefficients which should reflect the field content of the theory under consideration.