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Title: Classification of rank-2 four-dimensional $N=2$ superconformal theories
Plain: Four-dimensional theories with extra supersymmetry (a symmetry pairing each force particle with a matter particle) can be sorted by the shape of their space of vacua. The sorting is complete only for the simplest case, with one complex dimension.
Precise: Classify 4D $N=2$ SCFTs whose Coulomb branch has complex dimension 2 by their scale-invariant special Kahler geometry (fibrations by 2-dimensional abelian varieties, their stratification, and allowed Coulomb branch scaling dimensions), extending the rank-1 classification of Argyres, Lotito, Lu and Martone (2015-2016), and determine which geometries correspond to consistent SCFTs.
Settled by: A proven complete list of rank-2 Coulomb branch geometries with each entry matched to an SCFT or excluded.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: Rank 1 is classified (2016); rank-2 lists (Martone 2021; Kaidi, Martone, Rastelli, Weaver 2022) are not proven complete.
Posed since: (empty)