Are Soft Theorems Renormalized?

TL;DR

This paper investigates the behavior of soft graviton theorems at loop level in supergravity, revealing that a recently proposed soft theorem remains unrenormalized at one-loop order in specific dimensional regularization schemes.

Contribution

It demonstrates that the soft graviton theorem by Strominger and collaborators is not renormalized at one-loop in ${ m extbf{N}=8}$ supergravity, considering distributional aspects and dimensional regularization.

Findings

The soft theorem is not renormalized at one-loop in ${ m extbf{N}=8}$ supergravity.

The analysis accounts for distributional nature and regulator expansion priorities.

Results are obtained in $4-2\e$ dimensions for various orders of $\e$.

Abstract

We show that the distributional nature of soft theorems requires the soft limit expansion to take priority over the regulator expansion of Feynman loop integrals. We start the study of soft graviton theorems at loop level from this perspective by considering a five-particle one-loop amplitude in ${\cal N}=8$ supergravity. Surprisingly, we find that a soft theorem recently introduced by one of the authors and Strominger is not renormalized in this case. Computations are done in $4-2\epsilon$ dimensions and for terms of order $\epsilon^{-2}$, $\epsilon^{-1}$ and $\epsilon^{0}$.