Exceptional S-fold SCFTs are almost trivial

We study 4d exceptional S-fold SCFTs obtained from the 6d $(2,0)$ theories of type $E_{6,7,8}$. We show that all but one of these theories are discrete gaugings of free theories because they do not admit a consistent charge lattice. We compute the 1-form symmetry of the only interacting theory, the $k=4$ exceptional S-fold SCFT of type $E_8$, and find that it is trivial. Along the way we develop a consistency condition for the Coulomb Branch stratification of $\mathcal{N}=2$ SCFTs with characteristic dimension $\varkappa \neq \{1,2\}$ and show that the triviality of (most) exceptional S-fold SCFTs follows directly from this constraint.