The ABCDEFGJK of maximally strongly coupled $\mathcal{N}=2$ SCFTs

TL;DR

This paper classifies charge lattices and 1-form symmetries of certain $ =2$ SCFTs, revealing new structures and constraints, including the triviality of symmetries in some known theories and discovering potential new lattices.

Contribution

It provides a comprehensive classification of charge lattices and 1-form symmetry groups for $ =2$ SCFTs with specific characteristics, identifying new possible lattices and symmetry properties.

Findings

1-form symmetry groups can be of order 1, 2, 3, 4, or r+1 for certain SCFTs.

$ $-folds and Minahan-Nemeschansky SCFTs have trivial 1-form symmetry.

Discovered two sporadic lattices not realized by known SCFTs, with one potentially having a $Z_2$ 1-form symmetry.

Abstract

We classify all possible charge lattices and 1-form symmetry groups for $\mathcal{N}=2$ SCFTs with characteristic dimension $\varkappa \neq \{1,2\}$. For rank-$r$ SCFTs that are not stacks of lower rank theories the order of the 1-form symmetry group can be 1,2,3,4 and $r+1$. As an application of the classification we show that $\mathcal{N}=2$ $S$-folds and Minahan-Nemeschansky SCFTs have trivial 1-form symmetry. We find two sporadic lattices compatible with the Coulomb branch geometries $\mathbb{C}^5/G_{33}$ and $\mathbb{C}^6/G_{34}$ that are not realized by any known SCFT. The former, if realized, would have a $\mathbb{Z}_2$ 1-form symmetry and a non-invertible topological defect.