Duality Symmetries and G^{+++} Theories

TL;DR

This paper demonstrates that non-linear realisations of G^{+++} algebras encompass all duality symmetries of the on-shell degrees of freedom in related theories, highlighting their algebraic completeness and connection to supersymmetric form fields.

Contribution

It establishes that G^{+++} algebras, excluding B and C series, encode all duality symmetries and form fields of the associated theories, providing a unified algebraic framework.

Findings

G^{+++} realisations include all duality symmetries

G_2^{+++} accounts for supersymmetric form fields

A necessary root condition for G^{+++} roots

Abstract

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.