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

TL;DR

This paper investigates one-loop single soft scalar emission amplitudes in $ =8$ supergravity, providing evidence that the $E_{7(7)}$ symmetry remains anomaly-free at this quantum level.

Contribution

It offers an explicit calculation of one-loop amplitudes using tree-level recursion relations, showing the infrared finite parts vanish in the soft limit, supporting the non-anomalous nature of $E_{7(7)}$ symmetry.

Findings

Infrared finite parts of amplitudes vanish in the soft limit

Supports conjecture of no $E_{7(7)}$ anomalies at one-loop

Uses supersymmetric BCFW recursion relations for calculations

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.