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 N = 3 field theory, which is a non-perturbative S-fold of N = 4 super Yang-Mills theory. In this way, we can obtain as S-folds a new N = 7 (corresponding to 28 supercharges) W-supergravity and its 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 N = 7 supersymmetry algebra. Furthermore we also construct a four-dimensional heterotic S-fold with N = 3 supersymmetry. It again does not exist as perturbative heterotic string model and can be considered as the heterotic counterpart of the N = 3 superconformal field theories, which were previously constructed in the context of type I orientfold models.