Duality Symmetries and G^{+++} Theories

Understand

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories.

• This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory.
• We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.