SCFT/VOA correspondence and R-twisted reductions of $(A_2,D_{3n-2})$ Argyres--Douglas theories

Abstract

We study the SCFT/VOA correspondence for the $(A_2,D_{3n-2})$ Argyres--Douglas theories with $n\geq2$. From the matching of the central charges and the equality of the Schur index with the vacuum supercharacter to all orders, we propose that the associated VOA is the logarithmic doublet algebra $\mathcal A(4n-2)$ of Feigin, Feigin, and Tipunin. For $n=2$, this correspondence was studied in detail by Buican and Nishinaka, and our proposal extends it to $n\geq3$. Using the Nahm sum expression for the vacuum supercharacter, we further propose a family of 3d $\mathcal N=2$ abelian Chern--Simons matter theories that flow to the 3d $\mathcal N=4$ SCFTs obtained by the R-twisted circle reduction, generalizing the $n=2$ construction. We determine the monopole superpotential and show that the Coulomb branch is $\mathbb C^2/\mathbb Z_2$ for every $n$. The superconformal index provides quantitative evidence for the proposed infrared fixed points, including the expected enhancement to $\mathcal N=4$ supersymmetry and the Higgs and Coulomb branch structure.