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We study a set of four-dimensional $mathcal{N}=2$ superconformal field theories (SCFTs) $widehat{Gamma}(G)$ labeled by a pair of simply-laced Lie groups $Gamma$ and $G$. They are constructed out of gauging a number of $mathcal{D}_p(G)$ and $(G, G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $Gamma = D_4, E_6, E_7, E_8$ and some special choices of $G$, the resulting theories have identical central charges $(a=c)$ without taking any large $N$ limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of $mathcal{N}=4$ super Yang-Mills theory upon rescaling fugacities. Especially, we find that the Schur index of $widehat{D}_4(SU(N))$ theory for $N$ odd is written in terms of MacMahons generalized sum-of-divisor function, which is quasi-modular. For generic choices of $Gamma$ and $G$, it can be regarded as a generalization of the affine quiver gauge theory obtained from $D3$-branes probing an ALE singularity of type $Gamma$. We also comment on a tantalizing connection regarding the theories labeled by $Gamma$ in the Deligne-Cvitanovic exceptional series.
S-folds are a non-perturbative generalization of orientifold 3-planes which figure prominently in the construction of 4D $mathcal{N} = 3$ SCFTs and have also recently been used to realize examples of 4D $mathcal{N} = 2$ SCFTs. In this paper we develo
We construct several novel examples of 3d $mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted
We propose a generalization of S-folds to 4d $mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration
In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 $mathcal{N}=2$ SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 $mathcal{N}=2$ SCFTs. The glob
We initiate a systematic analysis of moduli spaces of vacua of four dimensional $mathcal{N}=3$ SCFTs. Our analysis is based on the one hand on the properties of $mathcal{N}=3$ chiral rings --- which we review in detail and contrast with chiral rings