Are Soft Theorems Renormalized?

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 $\epsilon^{0}$.