Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories

TL;DR

This paper demonstrates that certain 4d $ abla=3$ theories constructed from 6d theories realize almost all exceptional moduli spaces associated with complex reflection groups, expanding the known landscape of such theories.

Contribution

The authors show that specific 4d $ abla=3$ theories can realize nearly all exceptional CCRG-moduli spaces and extend the construction to include twists and outer automorphisms.

Findings

Realization of almost all exceptional CCRG moduli spaces by 4d $ abla=3$ theories.

Extension of construction to include twists and outer automorphism quotients.

New examples of 4d $ abla=3$ theories beyond simple S-folds.

Abstract

It is expected on general grounds that the moduli space of 4d $\mathcal{N}=3$ theories is of the form $\mathbb{C}^{3r}/\Gamma$, with $r$ the rank and $\Gamma$ 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 $\mathcal{N}=3$ theory with moduli space labelled by an exceptional CCRG (excluding Weyl groups) has been identified. In this work we show that the 4d $\mathcal{N}=3$ theories proposed in \cite{Garcia-Etxebarria:2016erx}, constructed via non-geometric quotients of type-$\mathfrak{e}$ 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 $\mathcal{N}=3$ theories going beyond simple S-folds.