Spin-four N=7 W-Supergravity: S-fold and Double Copy Construction

In the present investigation we consider the possibility of having new massive, higher spin W-supergravity theories, which do not exist as four-dimensional perturbative models. These theories are based on a double copy construction of two supersymmetric field theories, where at least one factor is given by a $ \mathcal{N}=3 $ field theory, which is a non-perturbative S-fold of $ \mathcal{N}=4 $ super Yang-Mills theory. In this way, we can obtain as S-folds a new $ \mathcal{N}=7 $ (corresponding to 28 supercharges) W-supergravity and its $ \mathcal{N}=7 $ W-superstring counterpart, which both do not exist as four-dimensional perturbative models with an (effective) Langrangian description. The resulting field resp. string theory does not contain any massless states, but instead a massive higher spin-four supermultiplet of the $ \mathcal{N}=7 $ supersymmetry algebra. Furthermore we also construct a four-dimensional heterotic S-fold with $ \mathcal{N}=3 $ supersymmetry. It again does not exist as perturbative heterotic string model and can be considered as the heterotic counterpart of the $ \mathcal{N}=3 $ superconformal field theories, which were previously constructed in the context of type I orientfold models.