Exceptional S-fold SCFTs are almost trivial

TL;DR

Most 4d exceptional S-fold SCFTs derived from 6d theories are essentially trivial or free, with only one interacting case exhibiting trivial 1-form symmetry, as shown through Coulomb branch analysis.

Contribution

The paper introduces a new consistency condition for Coulomb branch stratification in $ abla=2,3$ SCFTs and applies it to classify exceptional S-fold theories.

Findings

All but one exceptional S-fold SCFT are discrete gaugings of free theories.

The $k=4$ $E_8$ S-fold SCFT has trivial 1-form symmetry.

Most exceptional S-fold SCFTs are trivial due to Coulomb branch constraints.

Abstract

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.