Beschreibung:
<jats:title>A<jats:sc>bstract</jats:sc>
</jats:title><jats:p>It is expected on general grounds that the moduli space of 4d <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math></jats:alternatives></jats:inline-formula> = 3 theories is of the form ℂ<jats:sup>3<jats:italic>r</jats:italic></jats:sup><jats:italic>/</jats:italic>Γ, with <jats:italic>r</jats:italic> the rank and Γ a crystallographic complex reflection group (CCRG). As in the case of Lie algebras, the space of CCRGs consists of several infinite families, together with some exceptionals. To date, no 4d <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math></jats:alternatives></jats:inline-formula> = 3 theory with moduli space labelled by an exceptional CCRG (excluding Weyl groups) has been identified. In this work we show that the 4d <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math></jats:alternatives></jats:inline-formula> = 3 theories proposed in [1], constructed via non-geometric quotients of type-<jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathfrak{e} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>e</mml:mi>
</mml:math></jats:alternatives></jats:inline-formula> 6d (2,0) theories, realize nearly all such exceptional moduli spaces. In addition, we introduce an extension of this construction to allow for twists and quotients by outer automorphism symmetries. This gives new examples of 4d <jats:inline-formula><jats:alternatives><jats:tex-math>$$ \mathcal{N} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>N</mml:mi>
</mml:math></jats:alternatives></jats:inline-formula> = 3 theories going beyond simple S-folds.</jats:p>