Identify the four-dimensional theories arising from non-class-S circle reductions

Identify the four-dimensional mathcal{N}=2 theories produced by circle reduction of five-dimensional SCFT fixtures that do not descend to four-dimensional class-mathcal{S} fixtures with regular punctures.

Background

The paper shows that some five-dimensional fixtures reduce to four-dimensional class-mathcal{S} fixtures, while others do not. In particular, a rank-one example with manifest B2 oplus B2 flavor symmetry cannot be represented by the relevant regular-puncture data because the corresponding four-dimensional setup is bad and contains a deformation not generated by a class-mathcal{S} puncture.

The authors state that the circle reduction of this example should be another kind of four-dimensional mathcal{N}=2 SCFT, but do not identify it. They mention possible relations to theories arising from hidden Higgsings, leaving the identification unresolved.

References

Hence the circle reduction of the 5d SCFT at hand should be some other kind of 4d $\mathcal{N}=2$ SCFT, whose study we postpone to future work.

— 5d SCFT fixtures  (2609.09007 - Zotto et al., 8 Sep 2026) in Section 1, Introduction; Section 4.1, 5d fixture that engineers non-simply laced flavor symmetry

From the point of view of the classification of 5d SCFTs, we have at least two open tasks, in increasing degree of difficulty: \begin{itemize} \item classify all 5d SCFT fixtures, organizing them into families labelled by their flavor algebras (with particular focus on the non-simply laced symmetries), following the work carried out for the 5d conformal matter cases, also relating them to known constructions of 5d SCFTs with non-simply laced flavor symmetry ;

— 5d SCFT fixtures  (2609.09007 - Zotto et al., 8 Sep 2026) in Section 8, Outlook