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

TL;DR

The authors identify an infinite family of interacting 4D $\mathcal{N}=2$ SCFTs, $R_{2,2N}$, arising from twisted $A_{2N}$ compactifications and reinterpret the strong-coupling limit of $SU(2N{+}1)$ gauge theories with specific hypermultiplets. Using the Hall-Littlewood limit of the superconformal index, they establish an S-duality $SU(2N{+}1)+\wedge^2(\square)+\text{Sym}^2(\square)\simeq Sp(N)+R_{2,2N}$ and determine the Coulomb-dimension data, central charges, and a global symmetry $Sp(2N)_{2N+2}\times U(1)$, which is shown to enhance in the interacting sector. In the $N=1$ case, they provide strong evidence that the fixture realizes the Argyres–Wittig rank-1 SCFT with enhanced $Sp(2)_4\times U(1)$ symmetry and no extra free hypermultiplets, including a precise match of the indices across the dual descriptions and a detailed analysis of the chiral ring. For general $N$, the HL index confirms $n=0$ hypermultiplets, saturation of unitarity bounds via chiral-ring relations, and a consistent Sugawara-like 2D chiral algebra, thereby extending the duality to the entire $R_{2,2N}$ family. Overall, the work expands the landscape of 4D $\mathcal{N}=2$ SCFTs by linking 6D twisted compactifications to new strong-coupling fixed points and clarifying their global symmetries and operator structures.

Abstract

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 $Δ(u)=3$ of Argyres and Wittig. Using the superconformal index, we finally pin down the properties of this theory.