A Family of \(4D\) \(\mathcal{N}=2\) Interacting SCFTs from the Twisted \(A_{2N}\) Series

We find an infinite family of \(4D\) \(\mathcal{N}=2\) interacting superconformal field theories which enter the description of the strong-coupling limit of \(SU(2N+1)\) gauge theories with hypermultiplets in the \(\wedge^2(\square)+\text{Sym}^2(\square)\) . These theories arise from the compactification of the \(6D\) \((2,0)\) theory of type \(A_{2N}\) on a sphere with two full twisted punctures and one minimal untwisted puncture. For \(N=1\), this theory is the "new" rank-1 SCFT with \(\Delta(u)=3\) of Argyres and Wittig. Using the superconformal index, we finally pin down the properties of this theory.