The footprint of E7 in amplitudes of N=8 supergravity

TL;DR

This paper investigates the E7 symmetry in N=8 supergravity, demonstrating that all tree-level amplitudes vanish when a scalar boson becomes soft, highlighting the symmetry's implications for scattering amplitudes.

Contribution

It provides a proof that all tree amplitudes vanish in the one-soft-boson limit due to the E7 symmetry, using explicit Noether current calculations.

Findings

All one-soft-scalar-boson emission amplitudes vanish.

Tree amplitudes vanish in the soft limit under E7 symmetry.

Implications for higher-order amplitudes discussed.

Abstract

We study the low energy theorems associated with the non-linearly realized continuous E7 symmetry of the on-shell N=8 supergravity. For Nambu-Goldstone bosons we evaluate the one-soft-scalar-bosonemission amplitudes by computing the E7 current matrix element on the one-particle external lines. We use the explicit form of the conserved E7 Noether current and prove that all such matrix elements vanish in the soft momentum limit,assuming the SU(8) symmetry of the S-matrix.This implies that all tree amplitudes vanish in the one-soft-boson limit. We also discuss the implications of unbroken E7 symmetry for higher-order amplitudes.