From U(1) to E 8 : soft theorems in supergravity amplitudes

It is known that for N = 8 $$ \mathcal{N}=8 $$ supergravity, the double-soft-scalar limit of a n -point amplitude is given by a sum of local SU(8) rotations acting on a ( n −2)-point amplitude. For N < 8 $$ \mathcal{N}<8 $$ supergravity theories, complication arises due to the presence of a U(1) in the U( N $$ \mathcal{N} $$ ) isotropy group, which introduces a soft-graviton singularity that obscures the action of the duality symmetry. In this paper, we introduce an anti-symmetrised extraction procedure that exposes the full duality group. We illustrate this procedure for tree-level amplitudes in 4 ≤ N < 8 $$ \mathcal{N}