Exceptional $\mathcal N=3$ theories

TL;DR

This work constructs and analyzes four-dimensional $\mathcal{N}=3$ SCFTs, including exceptional types, by embedding M5 branes on $T^2$ inside non-geometric M-theory backgrounds (U-folds) and performing S-fold quotients. It connects known $(\mathcal{N}=3)$ theories to six-dimensional $(0,2)$ $A$-type and, crucially, to exceptional $E_{6,7,8}$ theories via non-geometric $T^3$ fibrations and duality monodromies, preserving $12$ supercharges. The authors show explicit quotients that yield $\mathcal{N}=3$ in four dimensions and provide a field-theory interpretation in terms of $(0,2)$ dynamics, moduli-space symmetries, and duality enhancements. This non-geometric engineering expands the landscape of $\mathcal{N}=3$ SCFTs and suggests avenues for exploring duality defects and outer-automorphism twists in higher-dimensional theories.

Abstract

We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of four dimensional theories by using an extra discrete symmetry on the M5 worldvolume. Together with the M-theory U-fold description of $(0,2)$ $E$-type six-dimensional SCFTs, this allows to construct new, exceptional, $\mathcal N=3$ theories.