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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 of theories with less supersymmetry --- and on the other hand on constraints coming from low-energy supersymmetry. This leads us to introduce a new type of geometric structure, which characterizes $mathcal{N}=3$ SCFT moduli spaces, and that we call $triple special Kahler$ (TSK). A rank-$n$ TSK moduli space has complex dimension $3n$, and is singular at complex co-dimension 3 subspaces where charged states become massless. The structure of singularities defines a stratification of the TSK space in terms of lower-dimensional TSK manifolds.
We study the stratification of the singular locus of four dimensional $mathcal{N}=2$ Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Cou
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 study the Cardy-like limit of the superconformal index of generic $mathcal{N}=1$ SCFTs with ABCD gauge algebra, providing strong evidence for a universal formula that captures the behavior of the index at finite order in the rank and in the fugaci
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 $(G, G)$ c
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