The footprint of E7 in amplitudes of N=8 supergravity
  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. 
Renata Kallosh and Taichiro Kugo