A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry

Abstract

We study single soft scalar emission amplitudes of $\mathcal{N}=8$ supergravity (SUGRA) at the one-loop level using an explicit formula for one-loop amplitudes in terms of tree amplitudes, which in turn are evaluated using supersymmetric BCFW recursion relations. It turns out that the infrared finite parts of all such amplitudes vanish in the soft momentum limit, which supports the conjecture that $E_{7(7)}$ symmetry has no anomalies at the one-loop level.