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

TL;DR

The work explores a non-perturbative route to ${\cal N}=7$ four-dimensional theories by employing S-fold projections within a double-copy framework that combines ${\cal N}=4$ and ${\cal N}=3$ sectors, yielding a massive spin-4 ${\cal N}=7$ W-supergravity without a massless graviton. It extends the construction to string theory via asymmetric, non-geometric S-folds (W-strings) in heterotic and Type II setups, where the massless spectrum is completely projected out and the first massive level realizes the ${\cal N}=7$ Weyl multiplet content. The paper provides detailed operator-counting checks in both field theory and string contexts, demonstrating agreement between the double-copy and string-sfold pictures for the lightest massive states. It argues that these theories evade standard no-go constraints by lacking a perturbative Lagrangian description and massless sectors, and it discusses potential holographic connections and future directions, including questions of consistency and unitarity in higher-spin W-theories.

Abstract

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.